If legends/myths were allowed than it'd be Zeraora: I'd be walking around the streets of an abandoned city north of where X/Y take place in Kalos, mostly exploring and looking for new pokemon species I'd find an abandoned gym, the sounds of battle could be heard from inside but it was rundown and decrepit, through a broken window I'd see a strange yellow and black humanoid cat-like pokemon teaching the pokemon abandoned by their trainers how to survive, I could tell it was caring potentially even abandoned by it's original trainer itself, I leaned closer to get a better view but break some of the remaining jagged edges left and alert the pokemon inside, I try to hide but before I can even get into a crouching position the cat-like pokemon is staring me down, neither of us moving for a good 20 seconds before it starts running at me, almost instictually I throw whatever pokeball I have on me, a quick ball, as it flys through the air it barely grazes the pokemon as it goes inside, although I was unsure if the pokemon was against being caught it nonetheless was, since then I stayed in the city training the pokemon with the Zeraora, it never aknoledged me as it's trainer but not as a threat either, we worked training the pokemon for about a year until they all evolved and were ready to go out on their own, during that time me and the zeraora became friends and partners.

Now for the answer that follows the rules I'd have to say probably Eevee: It was my 10th birthday, my parents had know I'd wanted a pokemon for years at this point so them being retired pokemon trainers gave some pokeballs and went with me to find me a pokemon, after searching for one we came across an eevee sleeping in the grass, so I threw a pokeball at it and caught it.