Advice for new AMD cpu

Hello everyone! Im looking to upgrade my cpu in a month or so to improve my fps for games. Specs: MB: Asus Crosshair III Formula - CPU: AMD II x4 955 (3.2ghz) GPU: ASUS GTX560ti - 8gb 1600mhz ram. Do I have to upgrade the gpu aswell, or is it o.k? Price for the cpu doesnt matter, the AMD processors are quite cheap imo. I think my motherboard got socket AM3, but I see that alot of the AMD...