You might be in luck. TF2 gets a gold rating under WINE, but you'll want to to check the site out for any special configuration you may need to perform...
http://appdb.winehq.org/
There's some great games that run natively under GNU/Linux. Most tend to be lower on the eye candy side, but they're fun and engaging. Look around, and see what you find.
Best distro? There's no such thing. That's one of the strengths of GNU/Linux. Instead of forcing everyone through one square hole, there's something for almost everyone. Ubuntu is a good choice for a beginner. If there's something you don't like about it, ask around. There may be a fix, or an alternative that'll suit you better.
For size, 20gb+ is good. More is better of course, but 20gb should be comfortable if you don't get carried away installing stuff.