My team almost always has Tifa and Cloud in it. When Aeris is alive, I use her, because I really like awesome magic users, and she has very powerful magic, not to mention excellent defensive Limit Breaks. By the end of the game I usually stay with Cloud, Tifa, and Cid, because they have the best Level 4 Limits. My reasoning for this?

Cloud: Omnislash-15 hits.
Tifa: Beat Rush, Somersault, Waterkick, Meteodrive, Dolphin Blow, Meteor Strike, Final Heaven-7 hits.
Cid: Highwind-Can't remember the exact number.
Barret: Catastrophe-1 hit.
Nanaki: Cosmo Memory-1 hit.
Yuffie: All Creation-1 hit.
Cait Sith: Slots-too unpredictible.
Vincent: Chaos-Lose control of him.
Aeris: Great Gospel-Awesome, but she's dead.

Barret, Nanaki, and Yuffie all do the same amount of damage with their final Limits as they do with Slash-All, by the time their level 100. So I prefer the characters with Limit Breaks that are still useful.