I would suggest making a balanced team with this structure.
Charizard: This is what you got from Professor Oak, so use it. Gotten as Charmander.
Vileplume: You should be able to catch Oddish early in the game just before Misty's Gym. Caught as Oddish.
Lapras: Let's face it. This is the best Water-type you can find. Besides, the gyms where it would be good are really late in the game.
Raichu: This is good for dealing with Flying-types. Caught as a Pikachu.
Dugtrio: Catch one at Diglett's tunnel before you do the Vermillion City gym. It will help.
Hitmonlee: This Pokemon will be a powerhouse after you get it in the Saffron Dojo.
Well, this is the best help I can offer. If you want, you can replace Raichu with Zapdos if you don't mind using Legendaries. The only problem is that you need to get evolution stones to make Oddish and Pikachu reach their final stage. Good luck.