I think it changes since I like most of the characters. In my first game, it was Cloud-Tifa-Barret. On my second game, it was Cloud-Tifa-Red XIII. On my third game, it started as Cloud-Tifa-Aeris, and after (SPOILER)Aeris died, my party has been Cloud-Cid-Tifa/Yuffie/Red XIII.

If I had to pick my favorite party, I'd take Cloud, Cid and one of the female characters. I can't decide between them.