This is a Windows XP computer, so I'm not even sure I can run anything past DirectX 9 on it.
DirectX 10 and 11 cards operate fine under DirectX 9 on XP. I've been using a 4670 with XP for years now.
It's better to get something newer than 9800 or X800 etc since they don't have the UVD hardware acceleration and will largely rely on the CPU so you'd probably be left in the same position with those cards.
I'd definitely recommend getting something like a 3450 or maybe 4650 depending on price. Generally you do pay a premium for AGP versions look hard enough and you should be able to et something reasonably priced.