Trainer Red's team kinda sucks and is boring, it's like the most disinterested Pokemon Yellow team. ESPECIALLY HGSS where he stacks on a second Water type and adds to the Electric weakness.
I think it'd be cooler for his status if his team had a lot more rarer Pokemon from a player perspective, a team that was actually hard to get especially in Gen 2.
My Proposal:
Eeveelution
Snorlax or Tauros
Aerodactyl
Lapras
Steelix
Charizard
Why?:
Eeveelution is a one of a kind Pokemon per playthrough. (gen 2 evo probably)
Snorlax is a two of a kind, or Tauros which is a good Safari Zone signifier. I could go either way.
Aerodactyl, fossil.
Lapras, almost extinct Pokemon.
Steelix, harder evolution of a Pokemon that is already semi rare encounter in Gen 1.
Charizard, Red Starter and the only Starter that fits.
While this is mainly filled with "gift" Pokemon, it's ones that have more variety than just the Yellow starters and I think it makes for a more interesting team. This team wouldn't be that hard to make in Yellow, but it'd be harder in Gen 2, too, and I think that'd add to the cool factor. Yes, this team commits the sin of deciding choices Red did, but I think that's fine + stuff like Aerodactyl are just cool additions. I don't particularly like Charizard but it fits the most.
I also feel like this would have genuinely decent team synergy, there is still a big Electric weakness but now there's a Steelix and you only have two monotypes compared to 4 (Blastoise/Pikachu/Snorlax/Espeon). Also most of these are pretty good Pokemon on a singleplayer BST level.
Candidates I considered:
Dragonite, decided against it because Lance has like two and they share the battle theme song already, make the identity weakened.
Tyranitar, because I preferred Aerodactyl as a Rock Type.
Alakazam, I see this as more Blue's type of Pokemon.
Arcanine, same as above + Charizard.