I follow yami_Yuffie's way when making parties,Cloud as compulsory of course,so I'll just put the other two in each party.

Aeris/Tifa
Nanaki/Cid
Barret/Cait Sith
Vincent/Yuffie
when fighting ultimate weapon......Cid/Yuffie,because I already got their final weapons
when Aeris is dead......Tifa goes with Barret instead,so Barret goes with two people.

When Cid is the leader
Cait Sith/Barret(for sure)

When Tifa is the leader
Barret/Nanaki