Hello @Strykermaximus.
We always encourage players to use their favorite Pokémon during their journey. However, if you simply want to rush through story, then I suggest you use Gyarados and/or Gengar. These two are enough to defeat most of the gyms and the entire Elite Four.
Generally speaking, Nature, Ability, IVs, and EVs do not make much of a difference when going through story. For Gyarados you'd want high Speed and Atk and for Gengar you'd want high Speed and Spatk.
The rest of your team can be filled with any fast and strong-hitting Pokémon. A few examples are: Alakazam, Dragonite, Jolteon, Arcanine, Rapidash, Dodrio, Scyther, Pinsir. In addition to Kanto-native Pokémon, you can find and trade for many Pokémon native to other regions.
Hopefully this can help you out. If you have any further questions, please let me know.