There are many good old games I wish I have time to beat, forget about the new games, You are only missing the graphics.
I dont have a clear idea about your graphic card. If its a motherboard integrated 64mb then its really bad, but if its a Gefore 3 or ATI Radeon then you can play a good deal.
Here some general suggestions, these older games shouldn't cost very much, and you can buy them cheap used like ebay or half.com:
Solder of Fortune II - This is a less popular but one of the better fps I've played, it might require some power but it should be possible.
Other masterpiece you might know of like: Deus ex, the Thief series.
There is a small chance you can run Morrowind. Otherwize best to stick with 2D like Baldurs Gate II, Fall Out 2.
You can definitely run the older advanture games, like Grim Fandango and The Longest Journey, another two masterpiece.
I actually prefer to play my psx games on my computer rather than the console, because the emulator let me have more freedoms like screenshots and save states. It doesn't require so much to run those 3d psx games, you can try some of the japanese rpgs, FFVII, Saga Frontier II, Breath of Fire III and IV. Or if you like a bit of strategy Final Fantasy Tactics, or Suikoden, but this game is very expensive to buy.
