Thief/Ninja - Yuffie
Skills: Steal, Throw, Escape, Mug, Coin, Morph, Remove
Other Materia: Gil Plus, Pre-Emptive, Speed Plus
Limits: None
Blue Mage - Cait Sith
Skills: All(?) Enemy Skills, Manipulate
Other Materia: Chocobo Lure, Underwater
Limits: None
Black Mage - Red XIII
Skills: Fire, Blizzard, Thunder, Tremor, Bio, Fira, Blizzara, Thundara, Quake, Biora, Firaga, Blizzaga, Thundaga, Earthquake, Bioga, Comet, Freeze, Break, Tornado, Flare, Cometeo, Ultima
Other Materia: Magic Plus, perhaps Magic Counter
Limits: Lv.1 - spell (tier 1) hitting all enemies, Lv.2 W-Magic (tier 2), Lv.3 W-Magic, all enemies (tier 3), Lv.4 Quadra Magic (tier4)
Arcane Mage - Vincent
Skills: Demi, Mini, Blind, Confu, Slow, Demara, Silence, Toad, Berserk, Sleepel, Demaga, Slowaga, Stop, Death
Other Materia: None
Limits: Perhaps Hades or some unique spell that inflicts several status changes, or leave him with his original transformations.
On to the somewhat tougher calls...
Berserker - Barret (I'm not too happy with this, though it wouldn't probably be bad, gameplay-wise.)
Skills: X-Attack (after lots of AP), Flash
Other Materia: HP-Absorb (linked to Slash All), Cover, Counter Attack (probably multiple ones, with different leveling requirements), HP Plus
Limits: None
Notes: Will always wear accessory that inflicts the berserk status.
Monk - Tifa
Skills: Sense, Deathblow, 2xAttack, 4xAttack, W-Item
Other Materia: maybe Long Range (after lots of AP)
Limits: Default ones.
White Mage - Aeris (She would obviously suit a white mage very well, the only downside is her early death, after which the need for a healer doesn't exactly decline, so probably someone else should take over this role from the very beginning. Tifa would be a rather valid option, though it would be sad, regarding her unique weapons and limits.)
Skills: Cure, Poisona, Barrier, MBarrier,Cura, Esuna, Life, Haste, Regen, Curaga, Reflect, Wall, Resist, Hastega, Full Cure, Revive
Other Materia: Magic Plus, perhaps Magic Counter
Limits: Likely the same as the Black Mage.
Summoner - Aeris (might be more appropriate for her, since the usefulness of summons - excluding KOTR - usually decreases towards the endgame anyway.)
Skills: All Summons in the usual order, except of Hades, provided he becomes part of Vincent's setup.
Other Materia: Magic Plus, MP Plus, perhaps MP Turbo
Limits: Either simply free of charge summons or some exclusive ones or W-Summon.
Cloud - Well... hard to decide. I was planning on giving him some elemental swords but that alone won't do. Adding Mime would be an option, but still a bit clumsy for a main character. Then again, there are still some spells to be allotet, such as DeBarrier and Dispell. This and maybe a couple more of some newish skills, which could allow to break enemies stats for example, would be fine, I guess.
Cid - Don't really know, he gets aboard too late to make for an effective white mage, so I'd probably let him have Tifa's part and simply call it Dragoon. This would furthemore be fortunate, in that you wouldn't have to start out with all the melees.
So, any help/recommendations would be greatly appreciated.
My own suggestions :
Cloud : Paladin (Knight + White Mage). Starts out with weak white magic so by the end of disc one he should be a potent replacement for the next character. You could also give him elemental swords as it fits with the job description.
Aeris : White Mage. Cloud's later abilities would solve that issue.
Tifa : Monk.
Barret : Tank-type character such as a fighter or a berserker as you suggest.
Red XIII : I see him more as a blue mage/summoner type of character.
Yuffie : Thief works well.
Caith Sith : Bard/Dancer. So he's as useless at his job as he is in the game. Plus it kinda works with the megaphone.
Vincent : Black Mage. So much more fitting for Vinny.
Cid : Dragoon. All his limits fit too.