I can't use a 500 watt power supply and my system doesn't support a 64 bit OS. This is why I was looking at the card I mentioned. Right now I have a Nvidia 8600gt..
As long as the power supply bay in your case is a standard ATX form factor, there's no reason why you can't put a 500W or larger power supply in it. The extra wattage the PS is capable of generating is not going to harm anything if it isn't used. And your processor will run a 64-bit OS if you install it.
The only thing that might be an issue with putting in a card like a GTX 560Ti (if you choose to upgrade your current system and put in an adequate PS and Win 7-64) would be excess heat build-up inside the case - those cards pump out a lot of heat when running under load (as in playing Skyrim). You'd need to keep a close eye on GPU and CPU temps at first, and if they got to be excessive, install an extra fan or two inside the case to help with ventilation, and clean off your components with some compressed air to remove excessive dust if it's present.
I wouldn't go with a card much beyond a 1Gb 560Ti with that computer, though. Even with that card, you're going to be CPU bottlenecked. You might just want to save up a few more dollars and replace the whole computer. That's your call.