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At least three of my favorite Pokemon manage to make it in
>Blastoise
Has a high pressure Hydrocutter, can learn rain dance if its regular water isn't potable and can serve as water transport and even aerial transport in a pinch
>Pikachu
Quick and small to provide a lot of varied assistance, plus the electricity can power up any device as needed ranging from house appliances to generators
>Gardevoir
Can learn so many useful moves and can effectively back up the rest of the team with them, can learn thunderbolt, flamethrower, teleport, wish, psychic, etc and can also create very strong barriers
>Chansey/Blissey
Can heal and its eggs are a legit food source for the entire party
>Lucario
Pure convenience with its aura senses, can detect hostiles and it can fight pretty well
We find a decent place to shack up and ride out the apocalypse until it dies out, if it doesn't die out entirely we hijack a Yacht and go find a livable place