your resolution should fit well with 5770. honestly i'm not really sure if your processor will create bottleneck to your system but you can OC your CPU if you think the processor is holding you back. 3.0-3.2ghz should be fine. what is your PSU brand?
i see. well i think you can think about OCing your system later. right now your system should be able to use 5770. if you look around you can find cheap after market cooler for your cpu. just make sure your case have good air flow so the heat is tajen out properly out from your case
the card that you mention should be fine. i thought that many people opt for vapor-x because of the cooler. it came with small overclock but you can always overclock the card yourself if you want more performance.