Swampy, by taking a look at your specs there's a couple of things to consider when improving the video performance.
The first one is size. A ruler is your friend, measure how much space you have both for length and thickness. High end video cards can be 30 cm/12" long and even 3 card slots thick plus the air intake space needed below them.
The second one is power. Your rig has a 300 watt power supply which means you can't consider high end cards using that one. Hopefully your HP uses a standard size power supply with standard wiring which would allow you to upgrade your power supply, too. IIRC they're attached both with the four backplate screws and a latch inside the case - the space between the latch and the back plate being just one mm too short for a standard PSU! I've managed to omit the latch, it gives in enough.
There's decent video cards on the market that are both small sized and modest in their power usage. Some don't even have an external power connector. But if your power supply has a video card power cable, it gives you more options to choose from. Here's some alternatives for low powered/small sized systems:
http://www.xtremegaminerd.com/best-budget-entry-level-graphics-cards/. Notice that they won't make your system the best AH3 rig ever, but they'd definitely allow for mostly playable frame rates using default settings.
