I know the newer versions of D&D but didn't watch the show. I'm also not very familiar with the version of D&D on which the show was based. To make things make sense, consider how much Zelda changes with each incarnation. (Think of it as if I knew Twilight Princess and had to wiki everything about Ocarina of Time.)
To that end, I can try to offer suggestions and information about the game, but I'd be unable to try to GM and wouldn't really be interested in playing. Ordinarily I wouldn't post, but figured I'd at least try to help with the classes information.
Human characters generally follow along one of the following lines:
Cleric: A priest/ess of one of the gods who uses divine magic for healing, and is trained in non-edged weapons like maces and in armor. They're especially effective against undead.
Druid: One with nature, wearing leathers and keeping to stone and wooden weapons, they use the magic of the wild to heal and transform themselves into animals.
Fighter: Your standard warrior.
Magic User: Your standard wizard or magician.
Mystic: A martial artist, aka monk, if I'm reading this right. This gets written out of the game for a while, so I don't know if it fits the show.
Thief: MaiMizzu already claimed this and I'm sure knows what it is.
Some of the classes I've seen but am not sure if these fit into the show:
Bard: A wandering ministrel who dabbles in magic and knows all sorts of tales.
Paladin: A holy warrior who mixes the Cleric and the Fighter abilities and dedicates him/herself to law and virtue.
Ranger: Focusing either on dual melee weapons or a bow and arrow, the ranger tends to be more an agile fighter who eventually develops some Druid abilities.
I hope this helps out some.