So you are planning to get a new PSU, it's OK. You will have a better upgradebility.
Corsair is better, both Corsair 500W (CX500) and 600W (CX600, GS600) will nicely suffice the 6770. It depends on your budget on how much you will spend for the PSU.
EDIT: LOL sorry you have posted your budget. You may get CX600.