This is kind of a loaded question I'm afraid cause most people can't agree on this, it really depends on your play style.

Warriors - Great damage dealers and excellent tanks, they can equip heavy armor and shields as well as wield the best weapons in the game. They can be upgraded into the Knight Class which gains the ability to use low level white magic.

Thief - Is a mediocre class, they can use light armor and knives as well as some swords. They have no magic or skills whatsoever and are pretty terrible imho. Yet, they upgrade into the Ninja class which actually can equip some of the best armor and weapons in the game, as well as access to black magic.

Black Belts - BB can equip light armor and bangles and use Nun-chucks and Staffs as weapons. They have decent strength and HP but low defense, but their is a trick to them. If you unequip them after they reach level 10+ their damage and defense rise dramatically, they are meant to be unhindered by constraining armor and weak brittle weapons. They have a very high critical hit rate and multi-hit like nobodies business. They upgrade to the Master Monk which garners them slightly better M.Def stat growth and higher damage modifiers, but are mostly unchanged.

White Mage - self explanatory but it should be noted they are the only class that can use Heal All and Undead damaging spells. Their upgraded White Wizard class gives them access to spells like Arise and Holy.

Black Mage - Self explanatory, except unlike W.Mage he has no unique spells that Red Mage and Ninja can't use. His Upgrade Black Wizard class does get exclusive access to Death, Break, and Flare.

Red Mage - Is like a mix of Thief, White Mage and Black mage. He has a better equipment pool than thief but shares some of it with his mage brethren. He has access to all of the Black Mage spells but cannot use Heal All or the Harm spells that White Mage has, meaning as a healer he is restricted to the single target Cure spells. His upgraded Red Wizard class gets a few of the Black and White Wizard skills but none of the major spells like Holy or Flare. His equipment pool is more mage like in this form as well so he's not as good as an offensive fighter like Knight, Ninja, and Master Monk unless you give him the Masemune.

In my current file, I'm using a Warrior, Black Belt, Red Mage and Black Wizard which is a very offensive based party. I do have to rely on items a bit more than usual but it hasn't been that detrimental. A good party that most favor is two Warriors, a Red mage and a White Mage. It gives you a nice balance though I personally hate having to grind for more gil to keep the Warrior's equipment updated, so you may want to switch out a Warrior for a Black Belt. Despite what everyone says, Black Belts are actually really good (my BB is actually better than my Warrior currently), they just lack pizzazz because they don't need equipment and can't use spells, but a party of them can finish the final boss off in two rounds.