Edit 2: You must be part of this group in order to receive your first pokemon.
Edit: Gym Leaders do NOT pick. These are for trainers only.
There are some starters where there are very few of them so only early trainers can own them. As for the other starters there is an unlimited amount so anyone may start with those.
Here are the list of all starter pokemon:
*

Squirtle: Water type. Trainers: ~
Ask-Cookie-prince*

Bulbasaur: Grass type. Trainers: ~
Ask-Pryce(Pistachio)
*

Charmander: Fire type. Trainers: ~
AskPyroPrince*

Pikachu: Electric type 9 left ~
Ask-Horna*

Eevee: Normal type 4 left. trainers: ~
AskBurner(Shun),~
cartoon-girl2004(Sofie),~
bluestarproduction,~
Ask-WhillathePeacock,!
Ask-PrinceofPain(Max),~
ask-the-freak(shadow),~
AskSparkle-the-human*

Chikorita: Grass type. Trainers: ~
LightenDarkenPrince,~
AskEyelessServent*

Cyndaquil: Fire type. Trainers: ~
Ask-Allison-and-Gang(Allison)
*

Totodile: Water type. Trainers: ~
Teh-Nobody*

Treecko: Grass type. Trainers: ~
Ask-Bellanca*

Torchic: Fire type. Trainers: ~
Ask-Pryce(Abel),~
AmethystTruth,~
askflaimirus*

Mudkip: Water type. Trainers: ~
Ask-PrincessPastel,~
Ask-Molly-Hyoomen,~
AskHerbert*

Turtwig: Grass type. Trainres: ~
ask-NicoleY*

Chimchar: Fire type
*

Piplup: Water type
*

Snivy: Grass type
*

Tepig: Fire type. Trainers: ~
AskVesta*

Oshawott: Water type. trainers: *
eyelessprincessPlease comment and let me know which Pokemon you will like