1. A 5770 to 6850 is not much of an upgrade at all. I would go for a 6870 at least.
2. Make sure the ram you get has exactly the same specs as the original ram.
3. Your PSU will be fine with the new equipment, no need to upgrade that.
4. CPU Cooler. Cooler Master Hyper 212 EVO.
5. SSD. A 120 GB SSD for booting and holding your programs and OS would really make your system feel responsive.