Hmm, are you sure you can't spend more ( 50 $ I mean ) is it really tight ? HD 6850 is a good card and is about 40-50 % more faster than HD 5770. What games are you planning to play on this rig ?
I will play mostly WoW and LoL. I had to buy a monitor already, and that was $120. Now i'm looking at 810 for the computer plus another 50 for mouse and keyboard. So, i'm already sitting at $980, when the budget was $800. :-) I quickly learned that $800 was way to low for what I wanted.
Do you play anything else ( more grahically demanding, example: Crysis )
WoW or LoL isn't demanding, so I guess, the HD 5770 would do fine for you.
I have never had the chance to play anything more than WoW or LoL. My current setup is beyond awful. I do play on purchasing Portal 2 and The Orange Box. I'm sure I will get into more gaming with a better computer.