I have a 5770. In terms of what resolution to run games, anything new, I have to drop to 1400x900 or 1280x800 to use higher quality settings. I can't really run ultra. Anything from 2010 or older I can run on 1680x1050 and highest settings.
I'd still get whatever monitor you want, but you'll be scaling to lower resolutions for smooth gameplay.
But I agree, 5770 was and is one of the best bang-for-the-buck graphics cards.