I think the 2 best are
Dwarf hunter especially with the OG cinematic, which is also why my first toon was a dwarf hunter
And tied with each other are Belf Hunters and Mages. The rangers are some of the biggest lore the belfs have. Mages were one of the main classes from WC3
Then again every class a Belf could play when released in BC fit the lore for Them
Oh I’d actually kill someone to get a alliance-vulpera or void elf druid 
Um hello.
Undead Locks and Belfs mages
I have respect for goblin shammys they bribed the elements and were rewarded for it
…i’m still waiting for Tinkers for Goblins and Gnomes. 
Although it kinda helps more goblin and gnomish weaponary is starting to appear so us small guys can fit anywhere. 
Human male paladin. The biggest whitest problem ever introduced to the world lol.
note, I’m not white, but in fantasy lands like wow, I can pretend to be.
extra note, this is a joke.
Elf mage.
Gnome Hunter with mechanical pets
Draenei shaman. “Unbroken” is my favorite Warcraft short story.
One of my favorite quests is in Cata. In Deepholm, get a quest from one goblin shaman wanting to save his protege. Not cause he likes him, but cause he just happens to be wealthy, and if he (the protege) dies, he (shaman trainer) doesn’t get a certain percentage of the family wealth.
The Goblin who needed to be saved is a younger goblin, just starting out in Shamanism, and hasn’t learned about how goblins have their race has nearly inescapable air tight contracts and just willy-nilly gave a fire elemental a shoddy power bracelet and angered said fire elemental lol. After saving him, and turning in the quest (paraphrasing here) he mentions on sending the Young Gobbo Shaman to a Warlock Trainer just to see if he gets bound to being and Imp’s servant for S&Gs.
Lets go through for each race and pick an iconic class.
Classic races:
Alliance:
Human: Paladin. Gotta be paladin. Arthas, Uther, Turalyon, and more!
Dwarf: Warrior. Mountain Kings, baby. For Ironforge!
Gnome: Warlock. Because there’s no Tinkers, but this people prone to remarkably bad decision making? Definitely the most likely warlocks.
Night Elf: Druid. Do i need to explain this at all? I love Demon Hunters and think they’re iconic, but they’re not Perfect Examples of the race.
Horde:
Orc: Shamans. Thrall, but also their entire religion being shamanism. That it plays such a huge role to their society. Second choice would of course be Warrior.
Trolls: This one is hard for me. I’m gonna go with Priest because i think most Witchdoctor stuff tend to use Shadow Priest, and i think thats the most iconic.
Tauren: A left field pick of Hunter. A big part of Tauren culture as we were told was never wasting, using everything they had. They didn’t quite have a Nelf worship of nature, but a respect. I think hunter fits well with that.
Undead: Rogue. I dunno what to say. Undead rogues are iconic more for having played Classic than for any specific character to me.
Wow, that was quick. Now onto expansion races:
Burning Crusade:
Draenei: Paladin again. Sorry, i know their racial leader is a priest, and they were literally introduced to allow shamans on ally side… but its Paladin.
Blood Elf: Warlock, at least originally. The fel addicted elves making use of fel magics and fel bargains with fel beings? Yeah. Of course. Nowadays i lean towards Paladin for these guys as well, though.
Cataclysm:
Worgen: Worgen is a hard one to pick for me. Is it Warrior, for the fury of the beast? Is it Hunter, for the werewolf and their wolf pack? Is it Death Knight so you can be a vampire werewolf? Yeah lets go with Death Knight.
Goblin: Warlock. Same reasoning as Gnomes, except you know their contracts are more abusive towards their demons.
Mists:
Pandaren: …It’s Monk.
Dragonflight:
Dracthyr: …
If you want to see me break down the allied races uh. I probably wont. I dont think I know much about any of them. Or care.
Great list well thought out and perfect
orc survival hunter looks like a warrior with pet
worgen heritage quest tell a story about worgen druidism, but worgen druid doesnt fit because worgen already is a wolf druid form. what about worgen monk? gilneas is next to scarlet monastery and worgen can appear to fight with claws
tauren with tauren totem, a DK