Halsin and Minthara - work as they are, though I gave Halsin one level of ranger for the weapon proficiencies (for the myrmidon shapeshift).
Jaheira - fighter / druid, since that is who she was in the original games.
Minsc - barbarian; he was a ranger in the original, but he could rage, and since wildheart barbarians can talk to animals, still fits.
Shadowheart - since she was chosen as a healer for the mission, cleric or lore bard. Either way, with high dexterity instead of the stats that she has.
Wyll - my favourite was warlock/sorcerer, played it as his sorcerous powers awakening when Mizora dragged him through hells. But storywise I think multiclass with bard, paladin or fighter all work.
Gale - wizard, his story is centered around him being one.
Laezel - berserker

Karlach - I don't think barbarian fits her story. She was a Baldurian city kid before the hells, and devils are lawful, so I'd expect their troops to be organized and disciplined, the opposite of barbarians. Fighter battlemaster, or maybe a ranger hunter.
Astarion - I liked him as a dexterity based fighter archer. I don't think his story is that connected to his class, so a lot of builds might work.