Just whatever does the job best, and looks good on the characters as well.

If you've got black magick gambits for magicks-geared characters, 'tis a good idea to give them staves and rods.

Vaan: Swords and Daggers
Basch: Axes/Hammers and Great Swords
Balthier: Guns and Bomb/Grenade-things
Fran: Spears and Bows
Ashe: Great Swords and Crossbows
Penelo: Katanas, Staves and Poles

fran - Katana
balthier - Poles/Sword And Sheild Combo
penelo -Sword And Rods
ashe - Whatever i find around from drops and chests
vaan - swords
basch - Swords

I'm trying to play through a game with the characters vaguely in classes, so:

Vaan (Thief) - Daggers, Ninja Swords, Katanas
Balthier (Gunner/Engineer) - Guns, Crossbows/Poles
Fran (Archer/Berserker) - Bows/Breakers
Basch (Paladin) - Swords, Greatswords, Spears, Katanas
Ashe (Black Mage) - Staves, Maces, Hand bombs
Penelo (White Mage) - Rods, Guns

I've totally neglected the reserve characters since everyone reached level 34, and only bothered to properly equip the 3 that matter.:

Balthier-Greatswords, guns, and crossbows.
Ashe- Katana (Masamune only).
Penelo- Bows, Mace + Shield.

I have all the top-level Black Magick spells except Ardor, and Ashe will normally cast Flare or Scathe if needed.

Balthier is more the heavy tank, Ashe slightly less armoured due to having a very low evade, even though both tanks have Maximillian and Magepower Shishak. She makes up for this by having a much higher combo rate thanks to Masamune. Penelo is geared to be the medic, as it were, and normally attacks from a distance.

I haven't suffered for having massively under-levelled reserves. Equip them all with bubble belt, and they should last long enough to revive the desirables.

Thing is though, different characters are most effective with different weapons. Unless all your main characters are the stronger "tank" type, they won't be that effective. Not to forget that you need some sort of caster to heal everyone during the battle. 2 tanks, 1 caster, works well.