Your processor is going to be your bottleneck, I'm assuming its a Core2Duo. No need to spend a lot of money, because that processor isn't going to be that great at 3D games. Check out the Best PCIe Card for the Money April 2011 article, then look for deals on Newegg.
Don't let the fanboys fool you, both ATI and Nvidia make good cards. If you choose one of the suggested cards in the TH article, you can't go wrong.
Depends on your resolution. For that PC though, I say if you're gaming at 1680x1050 or 1080p then a GTS 450 or Radeon 5770. A GTX 460 or 6850 is probably overkill even at 1080p as long as you use that old CPU. If a game is running slow it will more likely be the CPU hold it back. If your resolution is 1440x900 or lower, then go with a Radeon 5670.