Personally I've never rated Charizard, dare I say he's overrated? But I've always had a Golem that wipes it out with considerable ease.
I mean, given that there's a double-weakness there, that might make sense, but otherwise Charizard as a starter can be switched out if the opponent opts for a rock-type. You always figure that they complement some of the earlier Pokémon such as Pidgey, who can easily try evasive maneouvres and wear down the opponent's ability to attack, while Charizard can generally then scar them or finish them off, assuming that physical moves aren't preferred. As a special type attacker, they're quite notable and fairly powerful.
Playing through again recently I've realised that electric Pokémon don't give you much advantage unless you're fighting birds. Grass can counter the water, and rock slide seems to wipe out any flying type with a hit.
While Pokémon isn't akin to Rock-Paper-Scissors, except perhaps in name, this sort of thing does seem to be ignoring how even Pokémon types tend to have a weakness, and in that sense introducing new types doesn't necessarily help. The Rock type might help, as it has more resistances - though weak to ice, water, grass (two of the three main types), ground or itself, and fighting - but it is weak to opposed types, such as water, intermediate types such as fighting and ice, and itself, mostly, or ground, and in that sense when used for resistances can have some limitations.
That said, as Psychics did have negligible weaknesses, and the opponent using bugs might weaken them in most cases, you would generally perhaps want to include Hypno and Alakazam, who have different functions, and Alakazam is not necessarily better than Hypno at this. Perhaps a Hitmonchan may also be worthwhile, as it does allow for multiple checks, although this might depend on effectiveness otherwise.
Looking at your team, though, especially if Golem faints, possibly due to Surf, Giga Drain, etc., on the switch, or so on, you don't necessarily have that much which can be expected to last which can take down a Snorlax or Chansey on another team, apart from special attacks which they might fend off. As such, it might make more sense to go in with either a general attempt to impersonate Mewtwo with more general special attack, or to have an approach such as status moves which isn't necessarily deterred by these Pokemon, and can cause them problems to make switching in an immediate hazard.
A Charizard-Arcanine team, although usually checked by the defensive nature of water Pokémon, might also cause some issues here, as with many other sides, needing only some support alongside them to tear through most teams, and especially the status ones, once most resistances are eliminated. That would probably allow for checks to most prominent threads, perhaps of different kinds.
Not to give too much away, you would suspect that a Cloyster - a water-type Pokemon that makes sense given the moves and attributes of the type, and has an ice-type which protects it later on - and Vaporeon - who despite having clear weaknesses is mostly about still keeping solid defensively despite this - might be around there, if at least conceptually, along with the Hypno, Hitmonchan and Kadabra mentioned above, although Vaporeon and Cloyster would generally be a choice. There is some interest in: Bulbasaur, Beedrill, Growlithe, Psyduck, however, with the possibility of adding Mewtwo or Arcticuno if you want. If the birds are involved, a team involving a notable Zapdos, or possibly an Electabuzz, would also be possible. There's always room for attacking normal types, like Persian, as well as Poison-types, possibly alongside grass-types (who are victimised in such a team context, but oh well), and ghost-types, which would mostly tend to be Haunter or Gengar.
