Under $1300 is a pretty wide limit. I recently upgraded my computer from a stock Pressario to a solid gaming machine for less than $200.
I recently got a
XFX GeForce 8400 512MB that's serving me quite well, except the thing's as loud as a floor fan. I can't sleep without white noise, so this is fine for me, but might be a problem for you. It's powerful enough to run pretty much anything on the market (according to systemrequirementslab it can run Crysis, except my processor is too slow).
One thing I've learned in recent upgrades is to be very careful about what kind of motherboard to start with, specifically processor pin-type. The "industry standard" seems to change every six weeks, rendering any incompatable parts (still useful for older boards) simultaneously 'obsolete' and impossible to find. Expect to have a hard time rebuilding the thing again after more than a year, so build it to survive the game technology curve until the next time you expect to get a thousand bucks.
The other bit of advice I could add is to get a faster processor than you think you'll need. That requirement seems to be jumping higher recently. And make sure you get an adequate power supply and go all out on cooling. The more powerful a computer is, the more electricity is coursing through it.