Well you can get any full height card. The main things to look for, in terms of compatibility with your system, are
Card length: Hard drive, hard drive bays, cables, or SATA/USB ports on the motherboard could be blocked by too long of a card.
Card width: A card with a big heatsink and/or shroud might also block some necessary ports on the motherboard, or maybe the southbridge heatsink prevents such a big card to be installed.
Power consumption: There's probably only a 300-350W, which will restrict what cards you can get.
The good news is that you won't have to invest in old tech or old cards. You have a modern PCI-E x16 slot available so you can get any new card at a reasonable price.
Any card mentioned so far should be fine. Although without knowing the above restrictions, the safe bet is to get a card that doesn't require a 6-pin PEG power connector. Cards that don't require an external power connector don't need much power (and should run on your stock power supply) and aren't very big (so they should fit without obstructing anything). Also it's possible your power supply doesn't have extra power connectors for a video card that needs one.
So you should look at:
Geforce GT 240
Geforce GT 430
Radeon HD 5670
Radeon HD 5570
If you figure out size and power aren't a big issue, then you have free range to get just about any card.