BM Hunter, Prot druid, Blood DK, Prot Pala.
Those are definately the best! Maybe a prot Monk and than a Prot warri. Avoid any class that wears cloth or is a caster! Priest and mage are the worst classes for your wishes. A warlock with a tank pet also kind of works well, but not as good as the others.
The reason why those classes are the best and cost less problems are simple: Great survivability, can handle the biggest ammount of mobs compared to others, and because they are melees you avoid pulling anwanted additional mobs (for example by blinking into another group) of course tat doesn`t count for the hunter.
Running them as DDs (Feral, FrostDk, Retri Pala...) also works, but i do not recommend it for carefree afk botting.
Those named classes can level 1-100 without any class related deaths and using the singular routine.