The Moon for sure. It’s not enough, to do it all by yourself, but you could collaborate with the ESA which plans a moon village as a collaboration between many nations as well as private companies. One estimate for the cost of a lunar base is $10 billion - Moon Base Would Be Cheap with Help from Private Industry: Report - that’s from 2015.
I think the first priority though is to find out what is on the Moon, and for that we need some robotic explorers. So you could start by sponsoring a robotic mission to the Moon. Perhaps you could send your first robotic spacecraft to the Moon using Astrobiotics which is one of the more interesting Lunar X prize candidates for next year - they will take other spacecraft with them. It’s too late to join the Lunar X challenge as a new team but you could collaborate with one of the existing teams to help them to succeed and increase their capabilities, or you could just book a launch on a later mission.
Despite all the talk, I don’t think we will have space colonies in the near future, not in the next few years. And I don’t actually know for sure if we will ever. I think a good parallel is with the situation for Antarctica at the end of the nineteenth century. Someone could have come up with a plan to colonize Antarctica and if so they could have made a much better case probably than we can now for the Moon or Mars, for self sufficiency, so long as they were prepared to kill whales, penguins, seals etc - which back then nobody would have had any qualms doing. But - if anyone had done that, I think probably it wouldn’t have lasted long ,because it would be a hard difficult life, and why live in Antarctica when you can live somewhere much easier and go there for a year or two at a time supported by people outside Antarctica where it is so much easier to live, grow things, make things etc.
I think right now we are in a similar situation with space colonies. On paper it might seem they would work, but in practice, it would be so much easier to live on Earth and do most of the supplies from Earth, so I don’t think a colony right now would last long. It all depends on how easy it is to maintain. If a space habitat has to be renewed every couple of decades, it’s going to be very expensive, your one off billions of dollars payment will need to be repeated every few decades just to keep going. Probably also you need to send many spares to replace equipment as it breaks down along the way.
I think our priority right now is to explore rather than colonize. By finding out more we could prevent expensive mistakes a bit way down the road.
The best place for a colony though, if it were possible (which I don’t know if it is) might be the polar region of the Moon with 24/7 sunlight, ice nearby. Or alternatively the lunar caves. We need to know more about the Moon from the ground before we can judge their relative merits but the ESA certainly is focused on the lunar poles as the place to go.
If you do a head to head comparison, surprisingly, the Moon wins over Mars in many respects, even for resources for a start up colony, especially with new discoveries. Also the Moon has the advantage that it’s always at the same distance from Earth, easy to get to and back, with Hoyt’s cislunar transport system you can even set it up so you get materials back from the Moon with no use of fuel at all, exploiting its position higher in the gravity well of Earth, like rolling stones down a hill.
So anyway - I’d use a small amount for robotic missions first, and then join in collaboration with the ESA where a few billion dollars might perhaps mean you can contribute an extra habitat to the lunar village, or some extra shared capability, or help them to get it all underway sooner.
If the motivation is to go multi-planetary in an attempt to escape problems on Earth however, I’d say you can do a lot more with the same amount of money to protect the Earth - with half a billion dollars you could fund the Sentinel space telescope and detect most of the smaller asteroids in Near Earth Orbit within less than a decade.
But if the motivation is to explore and have humans in space, then the Moon is the place to begin I think.
Also in the case of the Moon there’s a chance of mining ice for water / fuel, of making solar panels in the high grade vacuum by vacuum deposition, mining various metals possibly including platinum, and you might possibly turn a profit by exporting to LEO or get some of your money back at least. That’s also possible perhaps for asteroids. Hard to see how you’d get any of your money back for Venus or Mars. And risks are far higher for them.
Also for Mars particularly, we sterilize all the robotic landers to prevent contamination with Earth life. Also there’s evidence that suggests it might possibly have habitats compatible with Earth life actually a few cms at most from the surface. If we continue to protect Mars from Earth life, I think myself that it’s not at all clear that we can land humans there, especially given the possibility of a crash landing. It might have interesting life or life precursors which we’d want to protect. Those who advocate Mars colonization are banking on us either finding that introduced Earth life will cause no harm to Mars, or deciding that we will stop protecting Mars from Earth life. However, when could we make either of those decisions? And what if we decide we want to keep protecting Mars once we know more? To do a sketchy first biological survey of Mars would require maybe 54 successful landers - just using an old estimate by Carl Sagan? So it will be a fair while before we can assess accurately what the effect would be of introducing Earth life to the planet. See How many years are needed to do a biological survey of Mars?
In the case of the Moon we already know that there is no life on the surface and it is classified as Category II meaning no special precautions are required to land humans there, or anything else, just document carefully what you do so that others who follow up know which parts of the Moon have had landigns / impacts which may have introduced Earth organics and other contaminants to the surface.
For more about reasons for going to the Moon first, and general background and why I think this is the time for space exploration and settlement and colonization is for a somewhat later date, if we do it at all (like Antarctica), see my Case For Moon First
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