I voted for No Secondary Type.
Fighting would add one massively helpful resist (Rock) and one somewhat useful resist (Dark), but would eliminate a good CAP resist (Flying). It would certainly add a lot of attacking coverage. I think Fighting would dominate the primary type. It would probably be easier to make a competitive Rock/Fighting pokemon. Rock is a really crappy type, and it is going to be difficult to make a mono-Rock pokemon competitively viable, without making it broken or weird.
From an educational standpoint, we will learn more about the Rock type in competitive play if we don't give it a secondary type. If we made a special Rock/Fighting pokemon, we might learn a few things about Fighting, since there aren't many special Fighters out there. But, Fighting gets a lot of play in the current metagame, so I don't think we'll learn too terribly much. On the other hand, almost everything we know about Rock comes from unstabbed move usage (Stone Edge & Rock Slide) and resistance/weakness to Stealth Rock. We know very little about using Rock as a primary STAB attacking type or from a defensive standpoint. For all practical purposes, we only have Tyranitar to learn from -- and it has ungodly uber stats and movepool. So, that's why I am voting for mono-Rock -- I think we'll probably learn a bit more about the metagame.
I have whole lot of other thoughts about Rock as the primary type, most of which pertain to bias and stats. I'll wait for those polls to voice my opinions there.