DVI-I and DVI-D are the same thing except DVI-I also carries analog signals for VGA displays and officially maxes out at 2560x1600p60.
HDMI 1.3/1.4 should be able to do 1920x1080p144 while DisplayPort 1.2 should be able to do 2560x1440p144.
So the best option would be DP 1.2 or better.