Hunter and Mage are most likely the best options for that. Druids and Locks are options as well but not as good as the first two.
Shamans are good if you want to heal in a 2man dungeon grind with say a War dps.
Rogues theres only a few options for solo dungeon stuff like BRD lockpicking but that’s far less profitable compared to say a Hunter solo farming Dire Maul.