Note that I will not be specifying which evolution of starter that each trainer listed uses. It would take a bit more time, and answering this is already going to take a lot of time, so, instead, I'm just going to tell which starter evolution line the trainer has. If you would like to know which starters each listed trainer specifically has, either check my source or ask in a comment on this answer.
Red/Blue/Yellow:
A list of trainers with starter Pokemon in Red/Blue/Yellow can be found here
Gold/Silver/Crystal:
Bulbasaur/Ivysaur/Venusaur:
Cooltrainer♂ Aaron
Cooltrainer♀ Megan
Cooltrainer♂ Nick
Picnicker Gina
Lass Linda
Pokéfan♂ Carter
Red
Charmaner/Charmeleon/Charizard:
Cooltrainer♂ Aaron
Cooltrainer♂ Allen
Cooltrainer♂ Kevin
Cooltrainer♂ Nick
Firebreather Dick (Gold/Silver)
Pokéfan♂ Carter
Red
Squirtle/Wartortle/Blastoise:
Cooltrainer♂ Aaron
Cooltrainer♀ Joyce
Cooltrainer♂ Kevin
Cooltrainer♂ Nick
Pokéfan♂ Carter
Red
FireRed/LeafGreen:
Bulbasaur/Ivysaur/Venusaur:
Beauty Olivia
Cooltrainer♂ Albert
Cooltrainer♀ Mary
Cooltrainer♂ Rolando
Picnicker Martha
Picnicker Tina
Aroma Lady Violet
Blue (If player chose Squirtle)
Charmaner/Charmeleon/Charizard:
Burglar Arnie
Cooltrainer♂ Rolando
Camper Chris
PokéManiac Dawson
PokéManiac Steve
Twins Kiri & Jan
Blue (If player chose Bulbasaur)
Squirtle/Wartortle/Blastoise:
Cooltrainer♂ Colby
Cooltrainer♂ Rolando
Camper Ricky
Swimmer♂ Garrett
Swimmer♂ Jerome
Swimmer♂ Mymo
Twins Kiri & Jan
Blue (If player chose Charmander)
Diamond/Pearl:
Turtwig/Grotle/Torterra:
Ace Trainer♀ Alyssa
Ace Trainer♀ Sydney
Aroma Lady Angela
Gardenia
Ace Trainer Sydney
Chimchar/Monferno/Infernape:
Ace Trainer♂ Dennis
Flint
Piplup/Prinplup/Empoleon:
Picnicker Karina
Pokémon Ranger♂ Jeffery
Veteran Edger
Platinum:
Turtwig/Grotle/Torterra:
Ace Trainer♀ Alyssa
Gardenia
Ace Trainer Sydney
Chimchar/Monferno/Infernape:
Black Belt Eddie
Flint
Camper Anthony
Pokémon Ranger♂ Jeffery
Piplup/Prinplup/Empoleon:
Picnicker Karina
Pokémon Ranger♂ Kyler
Rich Boy Jason
Veteran Edgar
HeartGold/SoulSilver:
Bulbasaur/Ivysaur/Venusaur:
Ace Trainer♂ Alton
Ace Trainer♀ Megan
Ace Trainer♂ Nick
Ace Trainer♀ Quinn
Picnicker Gina
Lass Linda
Pokéfan♂ Carter
Red
Charmander/Charmeleon/Charizard:
Ace Trainer♂ Allen
Ace Trainer♂ Alton
Ace Trainer♂ Kevin
Ace Trainer♂ Nick
Firebreather Richard
Pokéfan♂ Carter
Red
Clair
Squirtle/Wartortle/Blastoise:
Ace Trainer♂ Alton
Ace Trainer♀ Joyce
Ace Trainer♀ Kelly
Ace Trainer♂ Kevin
Ace Trainer♂ Nick
Swimmer♂ Randall
Pokéfan♂ Carter
Red
Chikorita/Bayleef/Maganium:
Ace Trainer♂ Cal
Cyndaquil/Quilava/Typhlosion:
Ace Trainer♂ Cal
Totodile/Croconaw/Feraligatr:
Ace Trainer♂ Cal
X/Y:
Bulbasaur/Ivysaur/Venusaur:
Professor Sycamore
Charmander/Charmeleon/Charizard:
Professor Sycamore
Squirtle/Wartortle/Blastoise:
Professor Sycamore
Sun/Moon:
Bulbasaur/Ivysaur/Venusaur:
Red
Charmander/Charmeleon/Charizard:
Red
Squirtle/Wartortle/Blastoise:
Red
Rowlet/Dartrix/Decidueye:
Professor Kukui (If player chose Popplio)
Litten/Torracat/Incineroar:
Professor Kukui (If player chose Rowlet)
Popplio/Brionne/Primarina:
Professor Kukui (If player chose Litten)
Ultra Sun/Ultra Moon:
Rowlet/Dartrix/Decidueye:
Teacher Emily (If player chose Popplio)
Professor Kukui (If player chose Popplio)
Litten/Torracat/Incineroar:
Teacher Emily (If the player chose Rowlet)
Professor Kukui (If player chose Rowlet)
Popplio/Brionne/Primarina:
Teacher Emily (If the player chose Litten)
Professor Kukui (If player chose Litten)
Let's Go Pikachu/Eevee:
Bulbasaur/Ivysaur/Venusaur:
Ace Trainer♀ Annie
Ace Trainer♀ Naomi
Picnicker Misaki
Lass Katrina
Lass Rena
Lass Sal
Poké Maniac Cooper
Coach Trainer♂ Kareem
Red
Charmander/Charmeleon/Charizard:
Ace Trainer♂ Christopher
Ace Trainer♂ Edmund
Ace Trainer♂ Tim
Lance
Picnicker Isabelle
Blue
Poké Maniac Damian
Super Nerd Erik
Squirtle/Wartortle/Blastoise:
Beauty Prita
Beauty Shirley
Beauty Tessa
Ace Trainer♂ Johnson
Camper Dustin
Cam
Green
Sword/Shield:
Bulbasaur/Ivysaur/Venusaur:
Honey
Charmander/Charmeleon/Charizard:
Leon
Squirtle/Wartortle/Blastoise:
Honey
Grookey/Thwackey/Rillaboom:
Pokémon Breeder♀ Chloe
Leon
Scorbunny/Raboot/Cinderace:
Pokémon Breeder♀ Chloe
Leon
Sobble/Drizzile/Inteleon:
Pokémon Breeder♀ Chloe
Leon
Source
I'm pretty sure that I got all of them, but there is a chance that I missed at least one. If anyone does notice that I missed any, please comment below and tell me what I've missed! I'll edit it in as soon as I can.
