Consider searching for used GPUS, I got myself a used 5870 for ~160$. I you can't find any I'd say the 5850. But frankly for 350$ you should be able to get a 7950.

Edit as for the rest of the components
-cheapest CPU you can find( can be a celeron or sempron) and a resonably priced motherboard
-a 380W-430W 80+PLUS Bronze or Gold power supply made by Seasonic/Kingwin/Super Flower
-any hard drive.