Now, this is neat… These are based on observations I’ve made playing the strategy games and World of WarCraft… Mind, a few of them have been pulled out of my backside.
Human: Paladin, Mage
Orc: Warrior, Shaman
Bronzebeard Dwarf: Warrior, Hunter
Forsaken Undead: Rogue, Warlock
Night Elf: Hunter, Druid or Priest
Darkspear Troll Hunter, Shaman
Gnome: Rogue, Mage
Tauren: Hunter, Shaman
Draenei: Paladin, Shaman
Blood Elf: Mage, Warlock
Greymane Worgen: Rogue, Druid
Bilgewater Goblin: Rogue, Mage
Pandaren: Monk, Rogue
Lightforged Draenei: Paladin, Priest
Highmountain Tauren: Hunter, Shaman
Void Elf: Mage, Rogue
Nightborne Mage, Warlock
Kul Tiran Human: Warrior, Mage
Zandalari Troll: Paladin, Druid
Dark Iron Dwarf: Warrior, Mage
Mag’har Orc: Warrior, Hunter
Mechagnome: Rogue, Mage
Vulpera: Rogue, Shaman
Dracthyr: Necromancer, Tinker 
…nah, Evoker
I’m being a little reductive in some cases, since there are still humans around from other cultures, orcs from this Clan or that (except for the Flowerpickers, Gul’dan hated druids), and so on, but… Here’s hoping this kind of helps you out! I’ll ask my friend to pitch in.