^ First of all, you need to check what kind of hardware your Compaq's motherboard will support: Does it have a PCI-express slot, or an AGP slot? Or does it even have a GPU slot at all? A quick search for the general specs reveals that your computer uses integrated graphics, so I can't determine if you can add-on a graphics card. You should also see if there's enough space inside the case to fit a graphics card. Compaq is one of those companies that custom-designs their case to be perfect-fit, not leaving much room for additions.
Once you figure out what you can add in, then you need to decide exactly what you want it for. If you have a fair amount of system memory (1gb+) and aren't looking for too much gaming performance, you can buy cards that have shared graphics memory, which will save you some money. Or else you might want to try to save up and get a new Geforce 8500 card--they run about $80 now, and will support next-gen DirectX10 games. If you're simply fed up with what you have now, then really any will do--just as long as you know you can install it into your computer.