In addition to the technological readiness point in Robert Frost's excellent answer, great analogy of a ski jump - I think we shouldn’t be focusing on colonization anyway. At present in space we are at a similar situation to the nineteenth century explorers visiting Antarctica. It’s a major challenge just to stay alive there. Our astronauts also need to be disciplined or they will die just as the earlier Antarctic explorers died of frostbite, and running out of food. Like Scott’s party that died within a short distance of provisions.

Cairn marking the spot where Scott’s party died on the return from their attempt at the South Pole.

We are nowhere near the point where we should think of setting up a colony in my view. We simply shouldn’t send 100 people at a time into space anywhere, so I’m dead set against using anything like the Elon Musk’s Mars Colonial Transporter for transporting people in large numbers anywhere in our solar system right now. It’s just far too dangerous. Most would die.

It’s like nineteenth century explorers sending 100 colonists at a time to Antarctica in an attempt to set up a city of a million there after doing calculations that seem to prove they could survive and be self sufficient (perhaps based on analogies of the Eskimoes and calculations of the numbers of whales, and penguins there were in Antarctic waters in the nineteenth century and the example of Shackleton’s crew that over wintered on elephant island living off the sea life).

We need careful astronauts who take many precautions, and who are good at responding promptly to instructions without question in such a dangerous environment. The astronauts make it look easy but every time they do a spacewalk, it is something that anyone without months and years of training could easily die from. And even then accidents happen such as the Italian astronaut who nearly drowned in his own spacesuit.

See also Spacesuit 3005 tries to drown an astronaut again and of course the famous Apollo 13 incident, also the time that a Progress supply misison collided with MIR in 1997. Progress M-34. We are bound to have many more of these and only disciplined, and highly trained astronauts can avoid disaster in those situations. And even they won’t always.

But there’s a larger question. Is that what we should be doing anyway - to turn as much of our galaxy as we can, into the closest possible (very poor) approximations to Earth that we can manage? I don’t think we should, not at this stage. We may miss much of value if we do that. It’s not at all clear that, even taking a totally human centered approach, that Mars or Proxima Centauri b is most useful to us as a po0r imitation of Earth.

They may be valuable to us as is. For instance Mars may have unique lifeforms that need the planet as it is now to survive. They may be vulnerable to introduced Earth life too. One of the most amazing things we could find in the field of biology would be some form of early life, to fill in the big gaps in our understanding of how life evolved. There are many ideas of what such lifeforms could be like, but we don’t have any examples of them. There is no currently extant life on Earth that could have evolved just from non living chemicals.

Modern life must have had many precursors because even the most primitive DNA based cell is far far too complex to arise from chemical precursors in one go. Also, our experiments in laboratories don’t get us anywhere near those early life forms either. We can’t create an ocean in a laboratory and leave it to evolve for hundreds of millions of years, as happened on early Mars as well as on Earth.

So, Mars just possibly might have lifeforms like that. It’s quite likely indeed, if you think that modern life took a fair while to evolve, given that Mars had only a few hundred million years to evolve life. Perhaps RNA based life, using the RNA based ribozymes rather than DNA and protein based rhobosomes for instance. That’s one suggestion for what we might find on Mars that came up in discussions of the smallest possible sizes of lifeforms after the ALH84001 discovery of a meteorite with structures that seemed like living cells but were too small for modern DNA based life. Or something more primitive, autopoetic cells - just metabolism but no exact replication yet. Or just replicating complex chemicals with no metabolism. We could find any of those on Mars. Or, no life at all, but a chance to study a planet with only chemistry and no life - again an opportunity we won’t have if we introduce Earth life to it.

Or it could be an advanced lifeform - microbial most likely or lichens, but still advanced, as we don’t know whether Earth life evolved unusually slowly, or unusually rapidly, or what drives evolution, and it’s possible that the difficult conditions on Mars as it cooled down actually drove innovation and evolution. It could go either way. Life like that could be vulnerable to Earth life also, just because it’s not evolved to cope with Earth life, or vice versa.They might not recognize each other as life.

I think it’s easy to see that early life would be vulnerable to introduced Earth microbes. They would just gobble it up as a food source and it would have no defences chances are, as after all, modern life must have made similar early lifeforms extinct on Earth long ago. And - there are many suggestions now of possibilities for liquid water on Mars, places where life might survive not just deep underground, but on the surface too, various habitats that may exist just in the top cm or two above the permafrost on Mars. I did a survey of the scientific literature for these a couple of years back, which you can read here: Are There Habitats For Life On Mars? - Salty Seeps, Clear Ice Greenhouses, Ice Fumaroles, Dune Bioreactors,... You may be amazed at how many ideas for habitats there are now. Not just the well known warm seasonal flows.

(Some people will say at this point that Mars life must be like Earth life because of meteorite impact transfer - but first that’s just theoretical, not proven, also it’s not at all easy for life to transfer to Mars, can only happen after the very rare giant impacts on Earth and then most lifeforms that could survive on Mars would not survive the transfer there, the life also has to find a suitable habitat after impact, not easy with present day Mars, and the bottom line is that so far, though experiments suggest that it is theoretically possible, we don’t know if any life has been transferred in either direction yet).

So, it’s the same for anywhere where there may be life including Proxima Centari b, the first thing is to find out what is there and learn about it. And introducing Earth life may turn what is an amazingly interesting planet into a poor attempt at a copy of Earth. Because - we don’t know how to terraform planets, and there is much that can go wrong. Proxima Centauri b, like Mars and more so, is nothing like Earth and Earth’s ecosystem transferred there would surely not survive. Intense radiation. One side always baked with the sun, other side dark. There may be lifeforms that live there especially if it has volatiles and a magnetic field to protect their atmosphere from getting stripped away. But that doesn’t mean that Earth’s ecosystem would work there.

Our ecosystem is dependent on many particulars of the way Earth works to continue. It is balanced for a particular distance from the Sun, particular levels of sunlight, composition of the atmosphere with oxygen in it. Transfer it to Mars and it wouldn’t work, it would be far too cold, trees couldn’t survive even in the tropics, and there’s no continental drift so not enough volcanic activity to return CO2 to the atmosphere.

Similarly transferred to Proxima Centauri b, again it wouldn’t survive, just a few hardy microbes I imagine would be all that’s left after a few centuries.

But there’s another yet larger issue. Do we want to colonize the galaxy? Just supposing we could set up a colony on Proxima Centauri b. Well that then means that potentially we can set up a colony anywhere in our galaxy, as stars like this and planets like that are very numerous. If we go ahead and do it then this is starting an unstoppable process that within a million years would fill the galaxy with humans.

That might seem great if you are into human colonization and you might imagine it like Star Trek or Asimov’s “The Foundation” novels. But we know that nobody else has done this yet, not an uncontrolled unstoppable expansion into the galaxy, or they’d be here already (as it’s extremely unlikely that another technological species evolves to technology within the same one million year period as humans, over the timescale of many billions of years). So perhaps that gives some pause for thought.

I think there’s a reason for that. If we fill the galaxy with humans, they won’t necessarily be careful peaceful people like the Star Trek adventurers. Or even the likes of the Borg.

The ones that grow in population most quickly and set up the most colonies most quickly would be the ones that fill the galaxy. And even though the colonization would probably start off as humans, these wouldn’t just be humans. If someone makes a genetically modified human, or a modified “uplifted” animal, or a machine, or cyborg (animal or human / machine hybrid) or modifies some extraterrestrial lifeform they find to make it more intelligent say, or more aggressive, into one that can fill the galaxy more quickly, that’s what will win the race. Also the ones that destroy other human colonies would probably win this race too. The sky would be full of human descendants and creations around every star, but - the most aggressive and expansionist of them would be the ones that win this race. If it is uncontrolled that is. And once colonization spreads to planets say a hundred light years from now, we’ll only know what was happening there a hundred years ago. Once it fills a galaxy, then there could be developments that we will know nothing about for a hundred thousand years. And if they are able to travel at close to the speed of light, then creatures or self replicating machines, or whatever, which have been developing for 100,000 years without our knowledge could approach us at close to the speed of light from thousands of light years away and we’d have almost no warning until this wave of creatures / machines arrives - either on Earth or on whatever other peaceful colony world there might exist by then.

So - I think we need to think carefully here before starting an exponential expansion into a galaxy, and I think any extraterrestrial intelligence would too. There may well be ways to do this safely. If so I think it probably involves an approach that has minimal impact on the galaxy, which might be why the galaxy seems to be totally untransformed and pristine. I think that’s exactly what you’d expect even if it is filled with intelligent species, if those species are forward looking (and perhaps the ones who are more reckless in character never are able to sustain space capabilities for any length of time).

The safest thing to do in terms of this long term future is to explore the galaxy robotically. First, send lightweight probes to all the nearby stars and their planets. Then we can also find ways to do safe replication of machines, once we can do that, tested in our solar system first, we can fill the entire galaxy with robotic sentinels around every star and planet. They can then tell us what they find, be our eyes and ears in the galaxy.

That’s something we can certainly do with Proxima Centauri b. We may be able to send tiny chip sized spaceships there at a fifth of the speed of light, so they get there in a couple of decades.

Meanwhile, for humans, I think the obvious place to begin is the Moon. Not Mars. We aren’t ready for that yet, and Mars is too valuable for us at this stage as a pristine planet that may possibly have native early life. I think we absolutely have to study Mars as it is now before considering transforming it, especially accidentally.

But the Moon - it’s perfect. It actually turns out to be more habitable than Mars in many ways. It is now thought to have resources we could use such as ice at the poles. Unlike Mars there is some possibility of commercially viable exports from the Moon other than ideas and intellectual property - which Elon Musk thinks is the only viable export from Mars. With the Moon we may be able to export metals, ice to LEO, we may be able to make computer chips and solar panels for space use, using the high grade vacuum there, far better than we can achieve at reasonable price on Earth, may also be our spaceship manufacturing center in the future for interplanetary spaceships since they don’t need to be built in small sections and sent up into orbit to be joined together - without an atmosphere and in the light gravity, you can just build the whole thing and launch it into orbit in one go. It’s a good place for maglev style railways again because of the high grade vacuum. It’s got caves, we know for sure, and there is evidence suggesting these caves could be up to kilometers in diameter in the low gravity there and some may be over 100 km long. That would make the volume inside one of the lunar caves as large as a typical O’Neil cylinder.

There is much of interest in the Moon and it is barely explored. I think this is where we should send humans at present. Robots first, lots of them, to explore the Moon. The first choice for a base may not be the best, we need to go there to look, also there is much of interest on the Moon just to find out from Earth using robots such as the caves, the polar ice deposits, questions about geologically young features on the Moon, search for those platinum deposits that Dennis Wingo thinks may be there as a result of impacts by metal rich asteroids including a large differentiated core of an asteroid 100 km in diameter that hit Earth in the early solar system. Anyway I could go on for a long time about the benefits of the Moon as a place to send humans.

And, we can experiment on the Moon with setting up habitats there. It’s got enough by way of volatile resources probably (still to be confirmed) to support a city of a million there. I calculated that there is probably enough water there for everyone in a city of a million to have as much as there is in one lane of an Olympic swimming pool - that’s a lot of water for a space colony. So plenty for first experiments in closed systems. With those we need to start small also I think, first ISS sized habitats, then larger ones, then maybe kilometer sized cities and space colonies, and even then I think we’d be nowhere near the stage where we can consider transforming an entire planet into a habitat. Further into the future if we import ice from the rest of the solar system we could cover the surface of the Moon with greenhouses and cities, if that is what we choose to do. Or we could build many habitats in space, spinning for gravity. There’s enough material in the asteroid belt alone to build habitats with a total land area a thousand times the land area of Earth, using the model of a Stanford Torus for them.

But even then, I wouldn’t ‘say go there to colonize right now. That is still like sending humans to colonize Antarctica in the nineteenth century. We still have no thoughts of colonizing Antarctica, though we have many people there, into the thousands especially in summer. It may be the same on the Moon. Or we may set up colonies there. I think it is just too soon to know yet.

Also right now I think our top priority has to be to protect and to save Earth. It is by far the most habitable place for humans in the solar system. Even with mega engineering, you’d have to strip away 99% of the atmosphere including all the oxygen, all of its oceans, most of the ice sheets also, remove its magnetic field somehow, and it would still be more habitable than Mars because it’s warmer, closer to the Sun apart from anything else. There’s nowhere else in the solar system remotely as habitable as Earth.

As Carl Sagan said in Pale Blue Dot

"The Earth is the only world known, so far, to harbor life. There is nowhere else, at least in the near future, to which our species could migrate. Visit, yes. Settle, not yet. Like it or not, for the moment, the Earth is where we make our stand."

I don’t think any of the discoveries since then have changed that. We do have a few possibilities for life in our solar system now. But not places where we can settle long term with anything like the ease with which we can live on Earth. Here even in the coldest driest desert, you can go outside without a spacesuit, and don’t have to protect your habitat with meters thickness of material, or to contain an atmosphere inside with an outwards pressure of tons per square meter. It’s hard to beat that.

It’s true Earth won’t be habitable indefinitely in the natural course of events. But half a billion years is enough time for humans to evolve a second time from the very smallest multicellular creatures. Maybe half a billion years from now it will be a priority to set up habitats elsewhere, for whatever intelligent creatures have evolved on Earth by then. Or they might have other solutions to the future hotter sun, such as shades in orbit, or moving Earth outwards in its orbit by various methods - as those are possibilities that are not far out of our reach already.

Or it might be that for a space faring species, that habitats in space spinning for gravity are the way to go, rather than planets, in which case there wouldn’t be much needed to change even when the Sun goes red giant, just move habitats somewhat further from the Sun and add more shielding.

Or might be that with fusion power, that we are independent of the Sun and can set up habitats in the Oort cloud with fusion powered “minisuns” and we’d hardly notice a red giant sun - or rather whatever creatures evolve half a billion years from now, or perhaps humans with immensely long lifetimes, living for hundreds of millions or billions of years.

If so - the Oort cloud is a vast region to inhabit, not just the trillions of people you could have living in space habitats built using materials from the asteroid belt - you are going up several orders of magnitude from that. Probably quadrillions or more. Which brings up those issues of what happens if those settlers colonize the galaxy. The Oort clouds mingle, it’s thought, so if we colonize the Oort cloud, we are almost bound eventually to colonize the entire galaxy. How could they be restricted to just our solar system or to the Oort clouds around a few stars? Maybe by then we’ll have some insights and breakthroughs that make it possible to do it safely for us and for the other intelligent species in the galaxy (if there are such) and other lifeforms?

At any rate, that’s not our priority at present. For more on this see Case For Moon First - Gateway to Entire Solar System - Open Ended Exploration, Planetary Protection at its Heart - online whole thing available to read for free.

It is also available as a kindle book on Amazon.com