Which connection type is the best for gaming at 1080p with a gtx 770 (HDMI,dvi,display port)?
They're pretty much all equivalent at that.
At 1080p 60hz, they have no difference besides hdmi which also carries audio.
It doesn't matter.
At that resolution any work. Display port and DVI are good for HD+ resolutions, but 1080P is easy to run on any of them.
At 1080p, they are all equal. HDMI and Display port will do audio.
Beyond 1080p, Display port and dual link DVI are better than HDMI and single link DVI.