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>Snorlax
No explanation needed.
>Zapdos
Apart from being the second best Pokémon in Gen 2, it can to some degree fill the role of Tauros in Gen 1, as long as the opponent doesn't have Rhydon or Golem. I'm by no means an expert on Gen 3, but it's apparently quite good there too.
>Cloyster
Clamp shenanigans with STAB Blizzard in Gen 1, best Spikes user by far in Gen 2. Again, not a Gen 3 expert, but it's a niche pick.
>Exeggutor
One of the Big Four in Gen 1 and a massive threat in Gen 2. Like Cloyster, it's not that good in Gen 3, but with those four, it's hard to go wrong in Gen 2 at least. They have amazing synergy and fill most roles between them (you're going to want a Normal-resist and a Whirlwind/Roar user, though), while also being viable individually in Gen 1.
For the last two teamslots, you have two different approaches:
1. Fill in the gaps to make your Gen 1 and Gen 2 teams as good as possible. The three roles you want here are the lead for Gen 1 (Alakazam/Starmie/Gengar/Jynx), the Gen 2 Normal resist (Golem/Rhydon/Gengar), and possibly Chansey, since it's just so good in Gen 1.
2. Pick the two Gen 1 Pokémon that are going to make Snorlax/Zapdos/Cloyster/Exeggutor into a decent Gen 3 team, if at all possible. I don't know which ones they are, but they're probably not going to be dead weight in Gen 1 and Gen 2.