Yeah, it will do very well at that res, another card you might be interested in is the 7750, performs very very near a 5770 and uses no external power connectors. Might be cheaper, I don't know the price of the 6770.
Oh and grab the 512 or whichever has the faster memory on it as it will perform better even though it might be less its still faster
My advice on this might be a bit off as I haven't looked into it with that card specifically but for the majority of cards its better to get less ram with a faster transfer speed than to get more ram with slow transfer speed (DDR3 vs DDR5 is a big jump in performance.)
If its ultimately a question between 512ddr5 or 1gb ddr3, go with 512. On the other hand if its 512ddr5 vs 1gb ddr5 go for the 1gb.