What games could I run on these computers?

Well if your SET on those two machines definetly go with the second one, it has a better video card...Personally I'd check out Craigslist for a custom built PC...Those computers will run it but it's performance would not be very good. Look for any PC with like a 9800GTX, 280GT

They both have **** video cards, they'd probably be able to run most games on decent settings if you give it a decent video card, but seeing as how your going for something cheap you could buy like a GTS 450 or 520 video card, but to be honest I don't think that comes with an Operating system. So in the end you'd end up spending a lot of money anyway between an Operating system, video card, and a network adapter if you need one, or anything else you might need. If you absolutely had to pick one i'd go with the second, but to be honest I agree with the other guy and think you should try to build one. You could look for a do-it-yourself kit, or just try to upgrade a current computer you have.