If it definitely has a PCIe slot, you'll be fine as far as that goes.
Next things you will need to worry about: What is your PSU's wattage? How long is it from the back of your case(where you plug, say, your monitor into) to the hard drive cage, or any motherboard obstruction that may be in the path of the PCIe slot?
Many HP desktops, unless rather beastly, will have skimpy PSUs. They will also likely have cramped midtowers with proprietary motherboards. This will cause many cards to not even fit. My mandingo sized 5870 would never fit in my old school HP computer's case. Heck, the nVidia FX5900 I had back then barely did.