It was either Pidgey or Rattata in Red. I can't remember which one, because I was so excited to finally have the game in my hands after following it since the Japanese release that I just went crazy with it.
Weirdly, though, I do remember Nidoran♂ being my third caught.
I honestly don't remember that well but it could have been Pikachu in Viridian Forest because I thought it was rare in Pokemon Blue. I also started out with Charmander for my second run after solo running Squirtle and blacking out so maybe I thought catching more mons would be better. This was even before the anime started so I really liked "fatchu" back then. Pidgey looked weird in R/B and so did Rattata so I vividly remembered not catching them at first.
I don't remember as it has been years since I played my first Pokemon game, but I'd like to say maybe Taillow was the first wild Pokemon I had ever gotten.