Dad would probably have a Growlithe/Arcanine, based on the pomspitz he inherited from his mom (and the fact that it seems like he builds a fire every other day).
Mom would probably have a cat Pokémon, based on all the house cats. Maybe a Liepard since she's wanted a Bengal for a long time, and the cat that stays in her bedroom has faint spots.
I think my sister would have a Jolteon since her Boston Terrier sort of reminds me of one.
And me? I guess I'd have a Meowstic-M. My gray cat isn't a Scottish Fold, but he's fluffy and didn't look too far off from Espurr as a kitten. I'm hoping the rumored "spiky ball of gray fur" Meowth form/evo is a closer match though.
Based on hobbies rather than pets, I guess my dad would have a Porygon/Porygon2 since he's into computer stuff, my mom a Carbink or Starmie since she collects glass, my sister... maybe Smeargle since she likes crafting (or Gallade/Gardevoir or something else that evokes Zelda), and I think I'd have a Mothim since I take photos of moths.