The power supply can handle any of these cards easily. EVGA is a good brand but for the best cooling I would recommend the ASUS DirectCU or MSI Cyclone. The factory OC on this card is impressive and make it a little faster than the HD5770(at stock);http://www.newegg.com/Product/Product.aspx?Item=N82E16814121394
Although you can save a bit of money and OC the card yourself if you want to(it's simple to do);http://www.newegg.com/Product/Product.aspx?Item=N82E16814121393
Speaking of overclocking an OC on your E6700 is a good idea. Putting it up to 3.3ghz should be very easy even on the stock cooler and will help in the more CPU intensive current games.