On my very first Pokémon game (I was 9, I believe), I caught only three Pokémon, and I only trained my starter for the most part. The result after beating the Elite Four was a level 87 Blaziken, a level 19 Taillow, a level 4 Ralts, and a level 20 Trapinch. Bogus, basically. Oh, and I caught a Numel with the Master Ball, completely oblivious to what it could do.
Since then, I've played Pokémon games more strategically, often building type-balanced teams that suit my expectations. I generally look for decent speed and movesets within each Pokémon. I try to build my team early on in the game, so I can access more of their moves without having to go to the Move Tutor or use TMs. I usually assemble a team of six by the time I reach the fifth gym or so. I generally put off filling my Pokédex until after I beat the Elite Four.
I play for fun, mostly. I used to battle over Wi-Fi quite a bit, but I've since stopped.