Harper, you're in luck. Your UT2k4 CD has a Linux installer on it.
I don't know about EVE online, is that a webbased game?
But yeah, Cedega works okay, Prey works great in it. Battlefield 2 kinda works... Half Life 2 works great.
If you are just starting, get Ubuntu.
www.ubuntu.com, then when you get a feel for it, switch to Debian.
I wouldn't bother with SuSE or Fedora, definitely get a Debian-based distro.