It's kind of hard to say. I think the first ever Pokémon-related game I played was a web-game called Pokémon Tower Defense, in which I chose Charmander.
However my first non-fanmade game was an online version of Pokémon Fire Red. I also chose Charmander there.
But my first TRULY official game was Pokémon Y (which I still play), and my starter there was a male Froakie (now fully evolved into Greninja).
Though before played Y, I started Pokémon GO, and I got a Male Pikachu as my first Pokémon. (there's an easy trick to getting Pikachu first: You walk around until Charmander, Bulbasaur, and Squirtle reappear 5 times, and on the 5th time a Pikachu will appear)
