If you are having a computer custom built or building it yourself, you may want to go with something like
this. Without a monitor (which you may not need too badly) it would be right in your price range, only slightly over with one.
To everyone who might look at that and say "X is better" or "Y is old, now Z is out": I suggest that you don't, unless you are willing to price your suggestions out and back them up with some benchmarks.
Ars System Guide has been around for years and is quite good. While not the greatest gaming machine in existence, this configuration is quite reasonable for playing most games -- and within budget.
