The sixth Gym Leader you will face on the road to collecting all eight Kanto Gym Badges is Sabrina. She is the Saffron City Gym Leader, specializing in Psychic Type Pokemon. Since you are now more than halfway to collecting all eight Kanto Gym Badges, Sabrina's Pokemon Team will be difficult to defeat regardless of your Starter Pokemon. This is because neither Bulbasaur, Charmander or Squirtle (and their given Evolutions) will have a type advantage over Sabrina's Psychic Types since they are all neutral against each other.
Because none of the Starter Pokemon will have an advantage over Sabrina, you might need to add an additional Pokemon or two on your way to Saffron City to better help you with Sabrina's Kadabra, Mr. Mime, Venomoth and Alakazam. The best Pokemon for this job is Haunter (found in Pokemon Tower), since Sabrina's Psychic Type Pokemon are weak against Ghost Types like Haunter. (But be advised that Haunter is also part Poison Type, making it weak to Psychic Types as well.)
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