First off, let's look at you're starters weakness... Blastoise (water) weaknesses are (electric and grass) you have no way of countering this, you need a fire and a ground type as a start and more coverage. I'd go for Arcanine or Flareon with this one, both can be obtained with Fire Stone and teach them both Flamethrower, that covers his grass weakness. A good ground early on is either Nidoking/Queen or Dugtrio all 3 are good Pokemon if used right Dugtrio is really fast but weak defense so it's all about you're needs.
Raichu's weakness is (ground) and Blastoise covers that, so you're good there.
Persian is normal type and I don't really recommend it, it's got a great move pool but weak stats. If you choose Persian go with Slash, Thunderbolt, Aerial Ace, and Faint Attack. As I said, he's not really good and I recommend a different Pokemon
So with what I told you Blastoise, Nido's/Dugtrio/Rhydon, and Raichu are you're only Pokemon. As I said, Persian isn't that useful. Now all you need is a Psychic, Flying (not needed but useful), and anything of you're choice just make sure it has type coverage.
Me personally this is what I would do.
Blastoise - Hydro Pump, Ice Beam, Surf, Iron Tail
Dugtrio until you got Rhydon. Rhydon - Earthquake, Megahorn, Rock Slide, Brick Break
Raichu - Thunderbolt, Rain Dance, Thunder (Thunder will not miss with Rain Dance), Body Slam
Arcanine - Extreme Speed, Flamethrower, Sunny Day, Aerial Ace
Dodrio - Tri Attack, Fly, Drill Peck, Steel Wing
Hypno - Psychic, Shadow Ball, Calm Mind, Toxic