My parents like small mountainous towns, so we would probably live either in Blackthorn "city" or Celestic town. Depends where they would find work. Till I would hit the mature age of 10, when pokémon trainers leave their homes, I would have to stay with them and couldn't choose a region.
Dad likes hiking in the mountains, so we would probably have a geodude or five and machop at home. Dad would never admit it, but he always wanted Onix, but my mom would never let him, because Onix is too huge.
Mom loves plants and gardening, she very practical and cares about the home, she would want pokémon that is both useful, pretty and doesn't make too much mess, so something like Sunflora, Roselia or Sprigatito would be hanging around our garden.
Both parents are very protective, so I wouldn't be allowed around dangerous pokémon. So no fire, electricity, poison... That would quite limit my choices and hinder my trainer carreer. They would probably purchase me something inoffensive and normal, like Eevee, Sentret, Bidoof or Buneary. Then I would have a local pokémon, that I would persuade my parents to keep, with a lot of crying. Probably Dratini or Ponyta. And a pokémon that my parents might never know that I have, but that all the cool kids in school captured as their first. Either Zubat, catterpie-tier bug, "pidgey" or "rattata" of the region.
I would never be allowed to leave home and try to become champion like other middle-school kids, would never have a chance to be serious trainer. I would graduate and would have to find a real job.