I'd say a new 7750 would be a good choice. You might be able to get away with slightly more, but this is a safe bet and still pretty decent performance. Also, more performance would probably be wasted on the old PC.
If you let us know what configuration your memory is in (1 stick, 2 stick, 4 stick) you can upgrade that pretty cheap. Also double check to make sure I picked out the right kind ... your PC should say if PC2 6400 is what it takes somewhere on it.
Yes I have 2 of those sticks with a total of 4 slots in the machine.
I will update that to 4 or 6 Gig RAM
So according to the Anandtech graph .. GeForce GTX 550 Ti should run fine on my system. If I am correct that can play most of the new games at medium to high res. Or am I expecting too much from my old horse.
If you had a name brand, high quality, power supply I would tell you that you could run a better card, however with a crappy HP stock supply I would not go above the 7750. You need the safety margin, because the unit likely doesn't actually put out anywhere near 365w.
If you have the money, you could go ahead and get a $40-50 power supply, then get any card you want. Granted, a better card will likely be bottle-necked by your processor/memory, but at least you wont have to worry about the computer burning up.