Upgrading graphics card- need advice!

So, my PC is getting a bit long in the tooth and I'm thinking on spending some money on a bit of a re-fit (I'd really like to play Skyrim on its highest settings). I built the thing myself just over three years ago- it has a Gigabyte EP45-UD3R motherboard, an Intel Core 2 Quad Q9550 processor, 4gb of RAM and (the weak link) a Radeon HD 4350 graphics card. I'm thinking of swapping out the HD 4350 for a GTX570 HD, but having been bitten by hardware compatibility issues in the past (I have an eight channel firewire soundcard gathering dust as we speak), i thought it best to ask some more knowledgeable people for some advice first!