From what I hear, G-Sync is a really cool technology (Basically, your graphics card talks to your monitor and vice-versa for a really smooth display), but I don't know if it's worth the extra cash. Your 770 will be able to handle > 1080p just fine. If you're looking for just one monitor, I would invest in 1440p (2560x1440) monitor. IPS boards are really nice too (for the color). In terms of cable, DVI and HDMI are pretty much the same, DVI just doesn't have sound, which shouldn't be an issue if you have your own speakers. Displayport (I'm assuming that's what DP means) is fine if your GPU supports it.
What's your price range?