I think it would be cool if they put all new classes in the game, or ones that were unspecified, but still showed uniqueness among the characters.

Bartz would be an all around balanced guy, but still clearly the best at melee attacks and raw strength.

Lenna would most likely be a white mage based character, but also throw in some insane speed for thief characteristics.

Galuf would have the ability to learn enemy skills, but have special attacks that would later be revealed to be unique to his world, which would make the skill transfer to Krile make sense story wise.

Faris would be able to cast black magic, but still have a decent amount of attack and defense since she is a pirate. Maybe give her some unique pirate skill things on top of that.

As for all other abilities? You can still customize the characters a bit by equipping some accessories that would grant them more skills. Alternately, they learn skills after collecting the crystal shards as usual, but keep them designated. My idea is more of an outline of how the characters would be when you first get them.