I mostly root for players, not teams, except for the dolphins. I always root for all the ex Hurricanes, even some Gators and some Seminoles once they make it to the NFL (since a lot of them came from the S. Fla. Area), ex dolphins and other personnel that I liked for one reason or another when they were playing in college.
I will always take one team over another when watching Sunday ticket, this usually involves in some way, helping the dolphins gain some real or perceived advantage playoff wise, and I always cheer against the Jets, Pats, and Bills.
NFC teams I cheer against are the ones that beat us in previous super bowls (Dallas, SF, and Washington come to mind), until they play each other, then I have a system for figuring things out, that probably only makes sense to me at the time.