I can't remember exactly which game I played first. Before I got my own Amiga, I played a few times at a friend's house, where we used to play games we could do with 2 players. Our favourites were SWIV, Lotus Turbo Challenge II and Speedball 2.
When I bought my first A500, I copied a few of his games, and if I remember correctly in my first box of 10 disks were Lotus II, Speedball 2, Twintris, Cubix, Prehistorik, SWIV, Rodland, Turrican, and Miami Chase (LOVE! that game - especially the soundtrack :-D )