I've went with Squirtle in Pokémon Blue version, as it was the game's mascot and whatnot. I did not regret selecting this Pokémon at all, as it was quite helpful in my eyes; it wasn't easy to take down in any way, and moves that it was able to learn were all-around great.
In my second run, I've selected Charmander, so that I could see how it's like when it evolves (of course, I've seen Charizard in anime, but at the time, have never tried it in-game). Just like Squirtle, it was equally as good. Back then, I have also thought fire-types to be strongest, in a way, so choosing this Pokémon did satisfy me, which is nice!
I was really fond of what they did in Yellow version; allowing us to not obtain any starter Pokémon in beginning, but get a hold of them later throughout. I believe it would be nice if they were to incorporate this method into some other game at some point in future.