I think most of VIII don't classify under classes since they don't have set paths on how they progress. Anyone can be anything. But if they did I say

VII
Cloud= Fighter or Warrior
Aerith=White Mage
Tifa=Monk
Barret=Gunner
Red XIII= I have no clue
Yuffie=Thief/Ninja
Cait Sith=Gambler

VIII
Squall=Warrior or Fighter
Rinoa=Sage
Quistis=Blue Mage
Zell=Monk
Selphie=Gambler
Irvine=Gunner

X
Tidus=Time Warrior
Yuna=Summoner/White Mage
Auron=Knight (If Steiner is then Auron is)
Rikku=Thief/Alchemist/Mime
Wakka=Gambler
Lulu= Obvious
Kimhari= Something/Blue Mage