Suddenly when I sat playing Xcom: Enemy unknown today I remembered some old FPS I played when I was younger. I don't remember it's name or exactly what the premise was but I have a few facts that might hint to what game it was
It's either post apocalyptic or SciFi with a very dark atomsphere (also graphically). You start the game by choosing one out of 3 characters, and if I remember correctly you could choose some big beefy guy, a gal of some sort (Amazonish I think but I am not sure, possibly red haired) and something else which I don't remember what was. Depending on which character you choose you get different weapons with basically the same functionality. One weapon I remember you could get was some sort of remote controlled spider robot bomb thingy. And IIRC the first level started outside some complex with the first enemy being some sort of turret firing red lasers