The story is quite simplistic: an asteroid hits earth and wipes out most of civilization (I don't think that's a spoiler - it happens in the first 5 minutes), then you get to run and drive around killing things for a while, and eventually the game ends. There's a spooky organization called "the Authority" who pop up from time to time, more frequent as the game progresses, and the whole thing is held together by a fairly simple set of objectives.
It's not a "deep story" game. The purpose of the story is to provide an excuse for killing things. A typical mission might go something like "these bandits have stolen something you need or are being a nuisance to a local settlement, so you get to go wipe them out".
Regarding it's FPS credentials, if you're more familiar with modern FPSs then you may be in for a shock. It's not a modern FPS, it's not like a typical military FPS. It's an old-school FPS with a focus on mayhem and carnage. Strategy? Tactics? Using your brain? Gettouttahere! It's not that kind of game.
Now, for some that's a refreshing breath of fresh air whereas others will run screaming from it. If it sounds like something you'd like (even as an entertaining diversion) then go for it - a lot of people are genuinely having fun with it, but a lot of others expected it to be something that it wasn't and are disappointed. Make your choice.
