That memory looks good, but if you want to be cheap 2gb is probably enough for most games - especially if you're running a 32-bit operating system, which will only recognize ~4gb total for the entire system. Just make sure you take out the 667mhz memory stick, or it'll slow down the rest of the memory too! If you want to be cheap, you could always get something like this
If it's only games that are causing problems, you'd probably be better off getting a newer graphics card. The 9600 GSO, while much better than anything integrated, is a very midrange card. A 9800GT or GTS 250 or GTX 260 would probably provide a noticeable increase in frame rate.
I went from a 7600GT to a 9800GT, and went from "playing" Crysis at lowest settings at 1024x768 (lousy CRT) to medium settings at 1920x1200. You probably won't see that large of a jump (your 9600GSO is a better card than the 7600), but it'll still be worthwhile.