Since my current playthrough is my first, I've been pretty disorganised regarding who uses what while exploring the different types, but a tentative grouping, as it has turned out towards the end, would be:

Vaan: Katanas, alternatively Bows for long range combat
Balthier: Guns mostly
Fran: Bows
Basch: Swords and Shields, alternatively Bows for long range combat
Ashe: Poles, alternatively Guns for long range combat
Penelo: Daggers and Shields, alternatively Crossbows for long range combat

I don't yet have a good grasp, only vague ideas, of what weapon types uses which stats etc. If/when I replay the game, I intend to decide on firmer classes for the characters and as a result, more determined weapon types for each character.