I'm not sure anyone is going to suggest integrated graphics if you're attempting to get playable frame rates out of TF2. I think your best bet is to repost this in the New Build section with a price range and see what people come up with.
well since he has some video cards listed, i doubt he is going to be relying on integrated graphics. anyway...i would say you would get some decent frame rates out of that set up. i have an 8600gts and a low end AMD (but twice the ram as you) and i can play GRID on almost high settings (1280 x 768 IIRC) with some decent eye candy @ about 30-35 FPS. id say you would be able to play it at atleast that on HIGH settings with that 8800gs. good luck!