The first console was the Sega Master System that my father had originally bought for my older brother, but gradually it became mine :) . It was around 1990, I was two, but if I recall correctly, I started playing when I was three. We started with three games "Ghost House", "Global Defense" and "Rescue Mission", with two more games, "Safari Hunt" and "Hang On" built inside the console.
The first console that was bought specifically for me was ten years later, a Game Boy Pocket, and the first game was "Pokémon Blue". I had a blue cartridge and a blue console :) .
The first console I bought with my own money was three years ago, it was a Wii. As it was a replacement for the Wii I had before and that died, I already had games for it. The first games I bought for the (original) Wii were "Sonic Adventure 2" and "Super Smash Bros Brawl".