Yep, what Kelly said.
For games, it's very, very, very important that you have a good graphics card--preferably a 3D accelerated card. You can pick these up pretty cheap, but the built-in graphics of a low-end PC just won't cut it. (In fact, these days many games will refuse to install if they don't see a 3D-capable graphics card!)
An Athlon processor will cost you about as much as a Celeron, but give you much better performance.