I just played through red

Used
Charizard
Pikachu
Gloom
Vaporeon
Dragonite
Hypno

I beat the final guy of the elite four with just gloom and dragonair. The games easy you can use just about anyone tbh as long as you got a couple types

Dragonite is pretty useless I found because it takes forever to evolve and gets no real good moves until later (mine evolved into dragonite after I beat Gary for the final time which is also the very end). And I just killed the legendary because I was to lazy to spam poke balls. Plus it's kinda too easy if you use them.

Nidoking
Alakazam
Syther
Charizard
Pikachu
evee into w/e

Any set is good enough to beat the game... but if you want to thrash:

Charizard
Alakazam/Hypno
Starmie/Slowbrow
Golem/Rhydon
Exeggutor/Venasaur
Snorlax

if you want to use Zapdos or Articuno, drop Golem/Rhydon, since Charizard can learn EQ/RS. Mew/Mewtwo would come in place of Alakazam/Hypno ofc.

Some other good very pokémon that come to mind:

Gengar
Persian
Chansey
Tauros
Lapras
Jolteon
Magmar

In general, avoid Poison, Bug and Fighting Pokémon. Water, and Flying Pokémon are to be avoided aswell unless they are combined with something good.

Charizard, Vaporeon, Nidoking, Kadabra (obv alakazam if possible), Macoke (obv machamp if possible), Gloom (vileplume if you want to evolve it).

With Charmander as a starter:

I wouldn't pick Gyarados. Even though he's a beast in RBY, the special atk/special def split really hurt. If you teach him surf it'll do laughable damage.
I say go for either Vaporeon or Lapras if you can get a hold of either of those.

I'd pick up a Nidoran, either species is good as an early team addition. They work out during the end since they have a HUGE movepool, and they evolve very early.

I'd just not pick a grass poke as they have terrible coverage and very common weaknesses. Take an electric type instead if you want to take on water types. Magnemite/Magneton are great choices as they have a steel subtype, giving them a TONNE of resistances/immunities.

At this point you can opt for a Psychic, Ghost or even Fighting poke. The downside about all these is that you need to be able to trade to get the best of their kind to their 2nd evolution.

And last but not least: Snorlax. Huge special wall, tonnes of HP and packs a punch. You could also opt for Tauros, Persian or Dragonite here, but I prefer Snorlax.

Uhh, no steel types in red man.

HAUNTER