The largest factor is Power Supply wattage and motherboard slots available.
Video cards demand a fair bit from your computer's power supply, so you may have to look at upgrading. I always go 200w higher than the manufacturer's suggested rating, as they base it on a 'typical' hardware setup of a CPU, motherboard, 2 fans, 1 HDD and 1 optical drive. It's also good to be safe and get more so you have room to expand.
As for the motherboard slots available: you mentioned it's a Core2Duo which tells me the board uses PCI-Express slots for media cards. That's a good thing. There are three different types of slots that a card can fit into:
1) PCI-Express (PCI-e)
2) PCI
3) AGP
When purchasing, do NOT assume that 'PCI' is 'PCI-e', because they're DRASTICALLY different and will not work. It won't even fit, actually. Again, considering the age of your board (C2D processors are socket 775, which wouldnt use AGP) you'll want to grab a PCI-e type graphics card.
The rest is up to you.
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