The nice thing about 8 is that you can build pretty much whatever party you want and still finish the game.
Ideally though, you want:
One character who can pick locks
One character who can cast healing and curative spells (bard and gadgeteer can work just fine here)
One character with strong melee capabilities
That's really it. Some parties will be more effective than others, but as long as you've got those three things, you're set. (It can even be the same character, e.g. a Ninja.) One thing to note, however, is that the heaviest armor and heaviest weapons can only be used by Fighters, Valkyries, and Lords. Chainmail is pretty effective, but if you want a true iron-clad bruiser, it needs to be one of those three classes.