My first game was Red version, and my first pokemon was bulbasaur. (even though charmander has an advantage over evry other pokemon in the first part of the game, as scratch is more powerful than tackle.)
I've only ever owned one Pokemon game, and it was back when we only had 150 (technically 151) Pokemon.
Anyways, the game I owned was Pokemon Yellow, for Gameboy Color, and I didn't have a choice, and was stuck with a Pikachu that followed me around everywhere. I'm guessing it was inspired by the TV-show, as the Pikachu preferred to be outside his pokeball (nor did he want to evolve).