Yeah - Red Mage, Sorcerer, Berserker, Time Mage, Summoner, and Mimic (which you can't reach until the Third World). I'm too tired to come up with another one, so someone else give it a shot.
That would totally depend on what monsters the game would randomly throw at you, but I'd guess it'd be a group of Imps in the area just outside the first town
But I'm guessing that Garland (the first boss) is the answer you want
How many different airships do you get to use in FF3 (the real FF3, not FF6) ?