So I'm basically just going for a gaming rig that can run games like bf3, skyrim, minecraft, on decent settings but not ultra. Not interested in OC or SLI really. Trying to keep it under $1000 as best as possible lol, but yea need some opinions .
One of the reasons that people like HDMI is that it has sound built in. Since you are getting a monitor with speakers this may be handy (prevents running two cables). I'm not a fan of having speakers built in, thus I don't, so DVI works great. Unless you prefer the speakers on the monitor I'd get one without them and buy actual speakers, although this can be pricier.
Monitor with speakers:
1 DVI, 1 Sound
Montior without speakers:
Someone can correct me if I am wrong, but I believe that is one of the primary differences between HDMI/DVI.