Well, my first Pokémon game was technically Pokémon Colosseum, but everyone starts with Espeon and Umbreon, so I won't count that. My first REAL Pokémon game was Pearl, and I chose Piplup. Because Piplup is absolutely adorable, and I've always associated myself with water in many video games. I don't think there was much reasoning beyond that.
Pokémon Yellow-Pikachu...obviously.
When it comes to choosing then it was Leaf Green's Squirtle. I chose it because it was cute and Water types are my favorite
Crystal-Chikorita-idk why cuz I don't like Grass types all that much and I'm kinda sorry I didn't pick Cyndaquil
Sapphire-Treecko-rare exception to being a grass type I really like. I didn't like the other and Treecko's evolutionary line rocks!
Black 2-Tepig-because he's an adorable piggy and I like pigs and because I don't like oshawat or snivy and frankly I've kept him as is because I don't like any of their evolutionary lines
Y-I haven't played it yet, but I was so certain that I was gonna pick Fennekin...but after seeing Fennekin's evolution line and seeing how awesome my kid's Greninja is I may change my mind and pick Froakie
Charmander, because a kid picking out of a turtle, green frog reptile thing and a fire breathing dragon, is obviously going to go for the cool fire breathing dragon.