graphics card for old pc

Solution
I wouldn't go any higher than NVIDIA 600 series or AMD Radeon 200 series. Any of these cards may require UEFI which your motherboard doesn't have.

I would consider a newer platform/PC all together. Any half decent graphics card even from the 600 series will possibly be bottle-necked by a core 2 duo machine with only 1GB of RAM. Are you running Windows XP or Vista? You may also have issues finding drivers for the card as well.
I wouldn't go any higher than NVIDIA 600 series or AMD Radeon 200 series. Any of these cards may require UEFI which your motherboard doesn't have.

I would consider a newer platform/PC all together. Any half decent graphics card even from the 600 series will possibly be bottle-necked by a core 2 duo machine with only 1GB of RAM. Are you running Windows XP or Vista? You may also have issues finding drivers for the card as well.
 
Solution
It should work

- Small, should fit in case
- Doesn't require UEFI BIOS to boot
- Has Windows XP drivers available
- Doesn't require any extra power other than what comes in a PCIe slot which even a 10 year old PC should have. You should verify you do have a PCIe slot before purchasing it though just to be sure.