I separated the list by primary type unless stated otherwise:
NORMAL (37): (Normal/Flying-types are listed with the Flying-types)
Basic Stage (14): Tauros, Ditto, Snorlax (Baby Pokemon don't count), Dunsparce, Stantler, Smeargle, Miltank, Spinda, Zangoose, Castform, Kecleon, Bouffalant, Furfrou, & Girafarig
1st Stage (16): Raticate, Persian, Furret, Ursaring, Blissey, Linoone, Delcatty, Ambipom, Purugly, Lickilicky, Watchog, Cinccino, Wigglytuff, Bibarel, Sawsbuck, & Diggersby
2nd Stage (4): Slaking, Exploud, Porygon-Z, & Stoutland
Legendary (3): Regigigas, Arceus, & Meloetta
FIGHTING (12):
Basic Stage (6): Hitmonless, Hitmonchan, Hitmontop (Tyrogue is a Baby Pokemon), Throh, Sawk, & Hawlucha
1st Stage (4): Primeape, Hariyama, Mienshao, & Pangoro
2nd Stage (2): Machamp & Conkeldurr
FLYING (12): (Normal/Flying-types are listed here too)
Basic Stage (2): Farfetch'd & Chatot
1st Stage (6): Noivern, Fearow, Dodrio, Noctowl, Swellow, & Braviary
2nd Stage (3): Pidgeot, Staraptor, & Unfezant
Legendary (1): Tornadus
POISON (13):
Basic Stage (1): Seviper
1st Stage (9): Arbok, Muk, Weezing, Swalot, Garbodor, Skuntank, Drapion, Toxicroak, & Dragalge
2nd Stage (3): Nidoking, Nidoqueen, & Crobat
GROUDON (14):
Basic Stage (1): Stunfisk
1st Stage (9): Sandslash, Dugtrio, Marowak, Donphan, Hippowdon, Claydol, Gliscor, Excadrill, & Golurk
2nd Stage (3): Flygon, Rhyperior, & Krookodile
Legendary (1): Landorus
ROCK (18):
Basic Stage (3): Sudowoodo, Lunatone, & Solrock
1st Stage (11): Rampardos, Omastar, Kabutops, Cradily, Armaldo, Bastiodon, Probopass, Archeops, Barbaracle, Tyrantrum, & Aurorus
2nd Stage (2): Gigalith & Golem
Legendary (2): Regirock & Terrakion
BUG (30):
Basic Stage (4): Volbeat, Illumise, Shuckle, & Durant
1st Stage (18): Kricketune, Accelgor, Parasect, Venomoth, Ledian, Ariados, Forretress, Masquerain, Ninjask, Shedinja, Wormadam, Mothim, Vespiquen, Yanmega, Crustle, Escavalier, Galvantula, & Volcarona
2nd Stage (7): Butterfree, Beedrill, Beautifly, Dustox, Leavanny, Scolipede, & Vivillon
Legendary (1): Genesect
GHOST (9):
Basic Stage (1): Spiritomb
1st Stage (5): Mismagius, Cofagrigus, Drifblim, Trevenant, & Gourgeist
2nd Stage (2): Dusknoir & Chandelure
Legendary (1): Giratina
STEEL (10):
Basic Stage (2): Skarmory & Klefki
1st Stage (2): Steelix & Bronzong,
2nd Stage (2): Klinklang & Aegislash
Legendary (4): Registeel, Jirachi, Dialga, & Cobalion
FIRE (20):
Basic Stage (2): Torkoal & Heatmor
1st Stage (9): Ninetales, Arcanine, Rapidash, Flareon, Magmortar, Simisear, Darmanitan, Magcargo, & Pyroar
2nd Stage (5): Typhlosion, Infernape, Emboar, Delphox, & Talonflame
Legendary (4): Entei, Moltres, Ho-Oh, & Heatran
WATER (48):
Basic Stage (8): Luvdisc, Basculin, Alomomola, Lapras, Qwilfish, Corsola, Mantine, & Relicanth
1st Stage (27): Golduck, Kingler, Seaking, Vaporeon, Octillery, Wailord, Milotic, Huntail, Gorebyss, Floatzel, Lumineon, Simipour, Clawitzer, Tentacruel, Dewgong, Cloyster, Starmie, Lanturn, Azumarill, Quagsire, Slowking, Pelipper, Whiscash, Gastrodon, Carracosta, Swanna, & Jellicent
2nd Stage (8): Feraligatr, Politoed, Samurott, Poliwrath, Ludicolo, Empoleon, Seismitoad, & Greninja
Legendary (5): Suicune, Phione, Manaphy, Palkia, & Keldeo
GRASS (28):
Basic Stage (3): Carnivine, Maractus, & Tropius
1st Stage (14): Sunflora, Cherrim, Tangrowth, Leafeon, Simisage, Lilligant, Gogoat, Exeggutor, Breloom, Cacturne, Roserade, Whimsicott, Amoonguss, & Ferrothorn
2nd Stage (9): Maganium, Bellossom, Serperior, Vileplume, Victreebel, Jumpluff, Shiftry, Torterra, & Chesnaught
Legendary (2): Shaymin & Virizion
ELECTRIC (19):
Basic Stage (6): Plusle, Minun, Pachirisu, Rotom, Emolga, & Dedenne
1st Stage (6): Raichu, Electrode, Jolteon, Electivire, Zebstrika, & Heliolisk
2nd Stage (4): Ampharos, Luxray, Eelektross, & Magnezone
Legendary (3): Raikou, Zapdos, & Thundurus
PSYCHIC (24):
Basic Stage (5): Unown, Wobbuffet, Chimecho, Mr. Mime, & Sigilyph
1st Stage (8): Hypno, Espeon, Grumpig, Musharna, Beheeyem, Meowstic, Xatu, & Swoobat
2nd Stage (2): Gothitelle & Reuniclus
Legendary (9): Mew, Deoxys, Uxie, Mesprit, Azelf, Cresselia, Lugia, Celebi, & Victini
ICE (13):
Basic Stage (3): Cryogonal, Jynx, & Delibird
1st Stage (5): Glalie, Glaceon, Beartic, Avalugg, & Froslass
2nd Stage (3): Vanilluxe, Walrein, & Mamoswine
Legendary (2): Regice & Articuno
DRAGON (8): (I'm leaving out Rayquaza for obvious reasons)
Basic Stage (1): Druddigon
2nd Stage (3): Haxorus, Goodra, & Dragonite
Legendary (4): Reshiram, Zekrom, Kyurem, & Zygarde
DARK (13):
1st Stage (10): Umbreon, Mightyena, Liepard, Zoroark, Honchkrow, Weavile, Scrafty, Bisharp, Mandibuzz, & Malamar
2nd Stage (1): Hydreigon
Legendary (2): Darkrai & Yveltal
FAIRY (8):
1st Stage (5): Clefable, Granbull, Aromatisse, Slurpuff, & Sylveon
2nd Stage (2): Florges & Togekiss
Legendary (1): Xerneas
TOTAL: 336