Apart from Cloud, there are four times when you're forced to use another character. You need Barret for the battles with Hundred Gunner/Heli Gunner and against Dyne, Tifa for the time when Cloud is in Mideel, and Cid for when Tifa stays with Cloud.

I'd say go with Tifa, since she'll be in the party for most of the game. Most would say Cait Sith is useless, but his Slot limit would make things too easy. And although Vincent's limits make you lose control, the stats boosts and HP recovery make them useful.