The 7770 is plenty for that resolution, it can handle games at 1920x1080 on medium/some high settings. However the 7850 is a much much stronger card that will be much better in the long run, especially if you play on upgrading your monitor to a higher resolution.
For your resolution a 1GB HD7850 would do quite well. I don't think you'd be disappointed by the HD7770 either (although you might need to lower AA), so let your budget decide.
In either case, get a Seasonic[-built] PSU. A G360 would run either card, although with limited headroom with a HD7850. A Superflower-built unit like a Rosewill Capstone or Hive would also be decent. A good size range is 450W-550W, which would allow plenty of headroom, especially if you want to OC.