What processor would be good depends on your budget, since most newer processors won't bottleneck that 5770.
If your budget is tight, try the Athlon II x3 435http://www.newegg.com/Product/Product.aspx?Item=N82E16819103872
If you have more cash, bump up to an x4 635http://www.newegg.com/Product/Product.aspx?Item=N82E16819103882
If your budget allows, a Phenom II x4 would be the next step up.http://www.newegg.com/Product/Product.aspx?Item=N82E16819103809
(or add $15 for the black edition)
As for cooling, as long as you are not overclocking, the stock fans that come with any new processors are perfectly fine.
Also 650 watts should be plenty as long as it is a halfway decent brand of psu.