Classic Traveller was my second (after AD&D). I still remember leaving my mother shopping to head for the back shelves in the San Diego Naval Exchange in case a new Little Black Book had come out....
I'm not sure which of Gamma World (1e) or Tunnels and Trolls came third, but those had to be solo play since no-one else was really keen to try them. Runequest (3e) was a bit later, along with its BRP cousins like Ringworld. Then Shadowrun (1e).
It wasn't until college that I ran across my favorite, GURPS (3e); I picked up the Cyberpunk genre book as inspiration for my Shadowrun campaign, then saw and immediately bought the Uplift worldbook, and only then picked up the Basic Set.