I would say Druid, Shaman, Warrior and Warlock. Those classes have a high variety of abilities which you will have to decide on to use your GCD for depending on the situation and class(es) you are playing against.
However, there are other things that are more important in Vanilla WoW:
Knowledge about the game in general
Positioning
Consumables
Goodies (i.E. Skull, Trinkets, Engineering items... the list is pretty long)
Experience (there are people on this server that have played vanilla for 10+ years and obviously they are the best)