I attended some games as a little kid, but I don't remember them.
The first game I remember was in May 1998 (I was 9). My dad and I went together and sat in the front row above the RF wall and out of town scoreboard. There was something about that game that got me hooked, and I started following the Angels religiously. I can't even tell you if the Angels won or lost, or even who they played (maybe the Twins?). Although I do recall Jim Edmonds waving back at me from CF between innings (or maybe I imagined that).
1998 was pretty fun. The Angels went 20-6 in June, then fizzled out in August.