Hmm... Not sure. It was probably something on my friend's Nintendo 64... Or on second thought, I don't think she ever let me play and just made me watch, so maybe not.
The earliest game I REMEMBER playing was Mario Kart on the N64. It belonged to my cousins and my sister and I loved it so much. They live pretty far away so I only got to visit them once while they still had it, I think, but it was lots of fun.
The first game I ever played that I OWNED was Mario Kart: Double Dash!! for the GameCube. When we got a GameCube for Christmas we also got Mario Kart and Animal Crossing with it, so we played Mario Kart first since we loved the N64 one so much. And Animal Crossing came next.
You're certainly lucky to have parents who like to play video games!