You can get Bulbasaur, Squirtle, Charmander all of them.
A girl in Cerulean City will offer you her Bulbasaur if your Pikachu is in good spirits. The easiest way to do this is to give Pikachu a Potion when at full health over and over again. Pikachu's happiness will climb, and you'll hold onto the Potion. Venusaur, to whom Bulbasaur evolves into, is a fantastic Grass/Poison-type with good Special and balanced other stats that will fair better than a Vileplume or Victreebel on your team.
Officer Jenny, found in the heart of Vermillion City, will hand you a Squirtle after you get the Thunderbadge. Upon evolving into Blastoise, this Pokemon carries very balanced stats with an emphasis on Defense. Blastoise makes for a good alternative to Lapras or Vaporeon should you not be interested in either of those.
Right after the Nugget Bridge, a trainer awaits you on a plateau to give you his Charmander. The young Fire-type, who comes very early in the game, becomes a powerhouse after evolving into Charizard. The Fire/Flying-type dragon Pokemon learns powerful attacks like Flamethrower and Slash and has magnificent Speed and Special. Unlike in Red and Blue, Charizard gets access to Fly. A good alternative to Arcanine or Flareon if they don't tickle your fancy.
Hope I helped