What games in particular are you looking at playing?
There's three issues with upgrading your GPU:
1) That power supply is pretty much absolute bottom-end. At 250W you'll probably be have to go with a very low-end GPU - the kind designed for media centres rather than gaming (because a) It just won't have enough power to support better, and b) It won't have the power connectors to power better). So, you'd need to upgrade the PSU as well otherwise you won't see a lot of improvement.
2) This is less of an issue, but your CPU is going to be a bottleneck on the potential new GPU. You're not going to get 100% of the performance out of it since your CPU being quite old (i.e. anything on the 775 socket).
3) Space inside the case. The dimensions might be too small for the high-end GPUs.
What's your budget for upgrading? Expect about $40-50 for a suitable power supply, and then $40 (bare) minimum for a useful GPU.
Another question - what are the other specs of the system in question? Amount of RAM and the specific CPU are the important ones.
I had a quick look on Newegg, found this combo. $100 for a PSU and GPU, the latter of which will be orders of magnitude better.
Or if you have a higher budget, get this PSU
And this GPU
Which is $205 but with two $20 rebates for $165.