http://h10025.www1.hp.com/ewfrf/wc/document?cc=us&lc=en&dlc=en&docname=c01761434#N1129
Your motherboard has a PCI-E 2.0 x16 slot.
You have a mid-size case, which is likely to provide the physical clearance you need for many GPUs.
However, it would not be recommended to upgrade to any video card which requires auxiliary power, unless you also upgrade your PSU, as your current PSU is rated for only 350w. This is going to limit your GPU selection substantially.
You could upgrade your PSU and go for an auxilary-powered GPU. At that point, you will have spent a substantial amount of money and your system as a whole would not benefit all that much, as your CPU/MOBO/RAM combination would hold it back a bit.
You didn't mention your price range, there is a limited selection of GPUs in the sub-100-dollar range that don't require outside power and may provide you with somewhat better performance. That would be my recommendation, if upgrading the system as a whole is not an option at this time.