Monster Races Idea - Version 2:
Beast - Bat, Bear, Boar, Crow, Wolf, Fox, Saberlion, Tiger, Vulture, Rat, Bear, Panther, Hyena, Hawk, Eagle, Amazonian Warbird, Stymphalian Bird, Crocotta, Katoblep, Bull, Horse. Artemis gives bonuses vs Beasts.
Beastman - Boarman, Centaur, Satyr, Ratman, Lycantrope, Minotaur, Catwoman, Silen, Triton, Harpy, Siren, Tigerman, Jackalman, Desert Hag, Sphynx, Yeti, Yerren, Neanderthal, Anteok, Troglodyte. Ares gives bonuses vs Beastmen.
Reptilian - Turtle, Crocodile, Snake, Basilisk, Ichthian, Crocman, Wyrm, Gorgon, Salamander, Dragon, Cetus, Hydra, Dragon, Naga, Aunoran, Hydradon. Poseidon gives bonuses vs Reptilians.
Spirit - Elf, Naiad, Oread, Lampad, Oceanid, Dryad, Hamadryad, Nixie, Sprite, Djinn, Core Dweller, Fire Sprite, Ice Sprite, Pixie, Kelpie, Maenad, Spirit Wolf, Spirit Boar, Spirit Crow, Valkyrie, Eihenjar, Nine-Tailed Fox, Kobold. Hermes gives bonuses vs Spirits.
Insectoid - Spider, Arachnos, Mantid, Scarab, Centipede, Swarm, Crypt Worm, Karkinos, Antlion, Scorpos, Scorpion, Formicid. Athena gives bonuses vs Insectoids.
Demon - Imp, Cerberus, Orthus, Limos, Erynie, Euronymus, Shadowstalker, Sha, Machai, Spartos, Melinoe, Peng, Rakshasa, Vetala, Yaksha, Bilwis, Empusa, Keres, Oneiros, Lamia, Androktasia, Moros, Chthonic Horse, Stygian Hound, Epiales, Dune Raider, Sand Wraith. Apollo gives bonuses vs Demons.
Undead - Skeleton, Revenant, Mummy, Wraith, Eidolon, Phasma, Taraxippos, Gui, Bone Scourge, Tomb Guardian, Bhut, Draug, Shade, Phantasm, Ghost, Undead Dragon, Lost Soul, Banshee. Hecate gives bonuses vs Undead.
Earthborn - Cyclops, Elder Cyclops, Dvergr, Jotunn, Troll, Eldjotun, Gigantes, Elder Gigantes, Korybantes, Kuretes, Hecatoncheires, Dactyl. Zeus gives bonuses vs Earthborn.
Construct - Automaton, Bolt Trap, Fire Trap, Ice Trap, Lightning Trap, Spirit Trap, Poison Trap, Golem, Teracotta, Minoan Statue, Guardian Statue, Pharaonic Statue, Asgardian Statue, Siege Strider. Hephaestus gives bonuses vs Constructs.
Plant - Briar Ward, Forest Guardian (Treant), Bog Dweller, Fungoid, Junglecreep, Forest Colossus, Quillvine, Tomb Rot, Ascacophus. Dionysus gives bonuses vs Plants.
Lesser Deity - Minor gods and demigods, like Graeae, Charon. Mostly and uber-hero race.
Greater Deity - All gods in the game. Boss race.
Primordial - Ancient monstrosities like Tiamat, Typhon, Echidna, etc. Boss race.
Edit:
Human - Bandit, Mercenary, Cultist, Robber, Amazon, Brigand, Desert Raider, Assassin, Sea Raider, Pirate, Sellsoul, Zealot, Demonologist, Witch, Enslaved Human, Corrupted Hero: can be any class. (Alternative - Ares gives bonus vs Humans, Dionysus gives bonus vs Beastmen. None gives vs Plants, they are too few anyway.)