I'm not sure we should actually. At least - not until we have to - that is with some impending disaster to destroy the Earth. And though it's a popular thing in science fiction and in movies, in actuality nothing in nature is likely to make Earth more inhospitable than say Mars or Venus in less than a few hundred million years.
And - maybe best place to build in space would be a big domed habitat - on the Moon - or a huge space colony or a tensegrity sphere in the Venus atmosphere. But a big domed habitat in the middle of an Earth desert or Buckminster Fuller's "Cloud Nine" or a sea city floating on the sea would be far far easier to build than all of those.
And we don't bother to build those because there are many far easier places to build and to live in our Earth at present.
So - I think short of some big game changing new technology (such as say self replicating machines) - I don't think we are going to move a significant part of the population of the Earth into space any time soon. Because it just doesn't make sense to do that when there is so much to be done on the Earth.
And no matter how much we might mess up the Earth in the next few decades, it still remains our beautiful Earth so much more hospitable than any other planet in our solar system for humans, and likely to remain so for millions of years into the future. And - ideas such as terraforming Mars - they are so long term and uncertain (a mega technology project achieving it within thousands of years is very optimistic) - and so many things to go wrong - that it doesn't change anything.
But more than that is a wider picture - would humans colonizing space be good for the galaxy - or for ourselves long term? Maybe - but I think if we remain as we are then - hard to see it working with humans with the power of self replicating machines able to reshape the galaxy. We could easily become the ET monsters of our science fiction horror stories - for other ETs in the galaxy - and in the future for ourselves also. That is - if we don't destroy ourselves first - but I think actually - that it's more likely we destroy ourselves or rather - the space colonies at least.
Something has to change. If it is just the same old, behaving as we do on the Earth - I can't see it working.
And in short term - could they be peaceful - or would they war with each other? Any space war would surely end with all the colonies involved totally destroyed. So - we have to be peaceful in space and find other ways to resolve differences.
And even if peaceful, what about economics and politics - if vast potential wealth of space mining for instance leads to individuals and companies in space that are as wealthy as say the US or China. Would we end up with the whole Earth in debt to a few individuals living in space for instance? Or to a few mega coorporations?
It's hard to know what will happen as nothing in our history can prepare us for it.
But - that's not so much of an issue if we have only thousands, at most maybe millions of explorers in space - but don't aim to colonize the galaxy - at least not yet until we can figure a good way to do that without disaster for ourselves and the galaxy.
So - I think we should focus on exploring for now, not colonizing. And learn what we can. And try to answer that question first. Is there a way that humans can colonize the galaxy without disaster for ourselves and for other ETs? Is there a safe, peaceful way we can do it?
Until we have an answer to that, then I think we should focus on exploring and discovery rather than colonization. That is unless we find some disaster that does indeed threaten our survival - but that's not likely quite yet. Perhaps half a billion years from now or more, when our seas boil dry -then space habitats may seem attractive as easier places to live than the Earth is by then.
So - both the safest - and also most practical and sensible thing to do - in my view anyway - is to send as many people into space as we need for space mining (done with care about economic situation), exploration, scientific bases, tourism etc - all that fine. But not to try colonization yet. Just settlement - similarly to the way that we have humans living in bases in Antarctica - but nobody attempts to colonize Antarctica, and I think there is no hurry to colonize space either. And if we never do - just have a few thousand or a few million people in space ever - that's just fine, is no imperative to say we have to colonize space.
Any more than we have to colonize Antartica or the tops of the highest mountains, or the bottoms of the deepest sea trenches or the deserts. There are many places we don't colonize, and space may well be the same.
But may well have many adventurers and explorers and scientists in space settlements - even interstellar - quite possibly taking great care with colonization absolutely forbidden - if it turns out that there is no solution to the problem of colonizing the galaxy in a safe and responsible way.
Or eventually, we find a solution and can colonize the galaxy - before that happens I think we may need to change ourselves also - not just invent new technology. We need to be so confident in the peacefulness and wisdom of humans that we know for sure that we won't turn into ET monsters or unleash uncontrolled 3D replicating machines or biological creatures or cyborgs onto the galaxy. If not - given vastness of the galaxy and number of potential possiblities for something like that to happen - we surely need to take great care before contemplating leaving Earth and colonizing space permanently. and long term.