"Let's Go" chooses to stick with the original 151 Pokémon, which includes skipping popular evolutions that were introduced in later games, like Pichu. You'll start with either Pikachu or Eevee depending on which version of the game you buy, and several wild Pokémon are exclusive to each version, as has been the case in past Pokémon games.
The decision to include only the first generation of Pokémon is clearly weighted by nostalgia, but it also helps keep individual Pokémon from getting lost in the crowd of hundreds. "Let's Go" refreshes the old Pokémon by giving them access to a larger library of moves than they had in "Red, Blue and Yellow," making things less predictable and helping each Pokémon feel more unique.