Kitoath, thank you for asking!
I live for these Lore Race Class Combo questions!
I will be giving my top two favorite for each race!
Alliance Core Races
Human: Paladin & Mage
Humans were the first to discover the Holy Light on Azeroth and when they learned the arts of the Arcane from their High Elven allies they became potent wizards.
Dwarf: Warrior & Hunter
Dwarves are famed for the legendary Mountain Kings.They are also experienced mountaineers and the creators of the legendary boomstick.
Night Elf: Druid & Demon Hunter
Malfurion was the first mortal druid in Azeroth, and instructed his teachings to the night elven people. Druidism is deeply saturated in their culture and very way of life. On the flip side Malfurion’s brother Illidan formed the deadly yet controversial demon hunter order.
Gnome: Mage & Warlock
Gnomes were part of the first council of Tirisfal making them, plus they have a natural affinity towards the arcane. After the fall of Gnomeregan many gnome mages became embittered and learned the dark arts to take vengeance on any who opposed them.
Draenei: Paladin & Shaman
For eons the exiled Eredar now called Draenei were taught the ways of the Holy Light by the cosmic Naaru beings. Draenei are inherently born with light given magic. Other than paladin, it was Nobundo’s journey to the elements of Draenor that led to the practice of shamanism within their culture.
Worgen: Druid & Rogue
The Worgen curse originated from the Scythe of Elune and the arch druid Malfurion himself. Remnants of druidism survived within the Gilnean culture and they were known as the Harvest Witches. Every Worgen you fight within Gilneas is a rogue as well. Skulking around and pouncing on their unexpecting prey.
Alliance Allied Races
Light-Forged Draenei: Paladin & (Holy) Priest
The Light-Forged Draenei were separated from Prophet Velen. They became hardened veterans against the constant battling of the Burning Legion. They are even more zealous towards the Naaru and the Holy Light than the other Draenei. Literally infusing the power of the Light into their body through ritualistic tattoos.
Void Elves: Warlock & (Shadow) Priest
Magister’s fascination with the void led him and his followers to become one with it. It was thanks to Alleria’s intervention that they were not driven to madness. Shadow Priest Lore is literally connected to the Old Gods, and Warlocks summon Void walkers.
Dark Iron Dwarves: Priest & Mage
Dark Iron Dwarves have long practiced the ways of the Light and Void alike making them powerful priests. They are also known for their powerful sorcerers for it was they who summoned Ragnaros himself into the mortal realm.
Kul Tiran: (Outlaw) Rogue & Hunter
Kul Tiras is famed for its seafaring sailors, making outlaw rogue the perfect fantasy for accomplishing this. They also have a flare of colonialism and greatly favor the boomstick as their weapon of choice making hunter’s viable as well, when exploring new charted lands.
Mecha Gnome: Warrior & Mage
Mecha Gnomes are very technical minded, even more extreme than a regular gnome. The advantage they have over their gnomish brethren and sisters is robust mechanical parts, making them able to hit way harder in force. Warrior would be the staple, with mage being easily learned twice as fast due to their accelerated brain processing.
Horde Core Races
Orcs: Warrior & Warlock
Every Orc is born a warrior (I guess excluding peons). Everything about warriors and orcs are so intermingled in their culture they are one and the same at this point. Orc warlocks were also the most infamous and caused terrifying destruction not only to the Alliance but to their own home world, it’s how their signature green skin tone even became a thing.
Undead: Rogue & Warlock
The Deathstalkers under Silvanus forsaken are probably the most infamous of the many organizations under her banner. The Forsaken were the only horde race at the time that took to the ways of the warlock with open arms.
Tauren: Shaman & Warrior
The Tauren have also strived to be one with nature and preserve the balance of the Earth Mother. They also helped the orcs rediscover their roots within shamanism. Tauren totemic warriors were powerful shock troops during the 3rd War and very iconic.
Troll: Shaman & Hunter
Troll shamans are witch doctors, in fact the shaman totems and ability hex comes from the original unit within Warcraft 3. Plus there are so many themed shaman sets that are aimed at trolls. Trolls are also renowned hunters as reiterated within the books of the Shen’dralar halls.
Blood Elf: Mage & Hunter
Blood Elves have had eons of practice with the ways of the arcane. They are the Archmage race in the game. Their racials show this and now the mage class has included some signature abilities like summoning the phoenix heraldic icon of the Sin’dorei. They are also renowned rangers, Sylvanus halting off the Scourge is still honored within their culture to this day.
Goblin: Rogue & Warrior
Goblins love profit, and rogue exemplifies their culture perfectly. Swashbuckle pirates, SI:7 agents or the famed Gob Squad. Rogue the definitive goblin class. Goblin warriors are known as “bruisers” in many goblin towns.
Horde Allied Races
High Mountain Tauren: Druid & Shaman
Huln was blessed by Cenarius himself during the War of the Ancients, giving him the iconic “Druidic Antlers”. After the world was sundered we have reason to believe that this sect Shu’halo actually continued to practice druidism being they were gifted by the Druidic God himself. Shamanism runs deep within the High Mountain society especially with the Rivermane tribe and we see it a lot in game as well with key characters.
Nightborne: Mage & Priest
The nightborne have kept their highborne heritage in their need and practice for arcane magic. Thus making them a mage society identical to the blood elves. Uniquely, they also still have Elune worshiping sects giving them ties to the priestess of Elune of the night elves as well.
Mag’har Orcs: Shaman & Hunter
The Mag’har orcs represent the orcs and their pure oneness with nature. Characters like Great Mother Geyah and the Half Ogre Rexxar come to mind. Between the throne of the elements and how the frost wolves hunted the mighty clefthoof these two classes really do their ancient culture justice.
Zandalar Troll: Hunter & Shaman
Zandalari are known for taming the mighty dinosaurs of days long past. And they are deeply religious to their various loa gods making them excellent shamans. Plus all of that lightning magic also comes from their dealing with the Thunder King of Pandaria.
Vulpera: Hunter & Shaman
Vulpera of Vol’dun are expert survivalists having to become one with the perilous desert land making them natural hunters. Their leader Kiro is also a restoration shaman, which makes sense that tribal leaders would have an affinity with obtaining water.
Neutral Race
Pandaren: Monk & Rogue
The ways of the mystical monk hail from the Pandaren. It is they who honed and mastered the art of hand to hand combat and contemplative meditation. The Shado-pan are a famous ninja organization with the Pandaria that have protected its people for centuries.
Thank you again for asking this question. I eat this stuff up. You can also find out more too on Warcraft Wiki it’s a great place to obtain lore quickly.