My first computer was one I built from two non working computers. It was a 486 with a whopping 75 MHz clock speed. ?I would have to go with Half Life. Quake II would be a close second, and Doom gets the bronze. I always liked the Wolfenstein spoof level in Doom II. When you kill a Nazi, he shouts, "Mich lieben!" as he dies. Nice touch, but lousy graphics (which is understandable, since it was the early 90s after all). The original Quake was my favorite as a kid, but the OP asked about storylines specifically. I'll never forget the day I beat Quake on nightmare skill level...with no cheat codes!
Thanks @Kissel bixby for the unexpected trip down memory lane! ?
It was a DOOM machine!