I had a HD5770 on my C2D-E8400 (3GHz) and the CPU was bottlenecking even in relatively low-end games like Diablo 3: I reused my HD5770 in my i5-3470 and I'm getting a steady 60fps on it vs 40-50fps on the E8400. I would not recommend spending on more than a GDDR5 HD7730 (~$80) for such an old system unless you are planning to carry the GPU over to a (relatively) near-future rebuild.
You did not mention anything about your PSU so I will presume it is an old generic ~350W unit that probably wouldn't handle much more than a HD7730/7750 either - at least not for long.
With only 2GB of RAM and a relatively slow CPU, you will likely end up finding out that the GPU upgrade alone is not enough to get performance quite where you wanted it to be. While the GPU is a large chunk of the gaming equation, it can only do so much when the platform it is on is that old.