I'd second the notion of Ubuntu, but if you have an older box, you might check out Xubuntu. It's a little slimmer for older machines.
If you are new to Un*x, you might want to get familiar w/ the basic commands. There are plenty of sites that list them & are just a google away. Of course, there's always the man pages too.
I don't play any video games, so can't address that point.