Here's the problem with your class of machine:
http://h10025.www1.hp.com/ewfrf/wc/...3196&cc=us&dlc=en&lc=en&jumpid=reg_R1002_USEN
The motherboard does not contain any dedicated graphics expansion slots. So you can not use the video card standards of either PCI-e or AGP.
The good news:
Your motherboard accepts PCI cards. So you will have to ensure that whatever card you purchase, is a PCI one (and not PCI-e, huge difference and incompatible.)
Newegg.com has a decent selection of this type of card. All of these are PCI, cheapest to highest price order.
Newegg.com - Computer Hardware,Video Cards & Video Devices,Desktop Graphics / Video Cards,PCI
As Ken has said, you need at very least DX9 capabilities and other factors.
If you want, pick out something you think you'd purchase and post back which one. It will most likely work and we will tell you if it's good.
One further thing you should do before making any purchase is look at the back of it and tell us how many cards are attached? Does it appear that there are available, empty slots to be used? If you're comfortable opening the computer, have a look inside if you're not sure how to tell. It would be easier then.
You would really like anything in HD series by ATI. They can play Blue-Ray, if that's an interest. They are slightly more difficult to install because of power requirements, however. If you're looking cheaper and least expensive way/easiest way with very decent results for a non-gamer, 6200 is a good choice.