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My mother raised me and my sister as a single mom, with my dad sending fat checks. My mom didn't let us keep pets and I doubt she'd be able to feed another mouth so I wouldn't get one of those childhood Pokemon.
Some stuff happened and I had to live with my dad around age 10, and while he and my stepmom were pretty much rolling in cash I never got anything extravagant and instead only got used stuff (my first Pokemon game was Yellow version, played on a used GBA when Ruby was already out for example), so I think asking for a Pokemon would be out of the question, and a Starter is totally impossible even if it was affordable for my dad and stepmom.
We also moved around a lot, literally all over the east coast with travelling in between. I've always lived near water so I can see myself taking in a Marill somewhere in this timeframe without my parents knowing or caring. (They seem rare in Johto but really common in Unova) I got kicked out on my 18th birthday, so I moved to NY and have been here like 4 years. I could see myself buying a Pansear, which is probably treated like a discount Starter, and a Mareep or Miltank since there's a ton of farmland around Rochester and my aunt literally lives across the street from one.
As for battling, I go to fighting game tournies, I could see myself getting into battling at least a little, but not enough to do gyms or anything.
tl;dr
>Azumarill
>Pansear
>Flaafy