Well with an athlon 64 processor, a 250w power supply, and an x8 PCIe slot you are very limited. That thing can barely run facebook, I don't know what games you are hoping to play but anything more than about an 8800gt would get bottlenecked by the cpu. The 8800gt would require you to upgrade the power supply. an 8600 would work as is doesn't need external power but may be too long to fit in your case. There are also a few green models of the 9800gt that do not need external power if you can find one.
A radeon 6570/6670 also would not need external power, not sure if they would fit, you'll have to measure how long a card would fit.
Edit - also verify with the manufacturer of the card if it will work with on a pcie version 1 slot. most cards will but some wont.