Shame about the last results, very predictable
Anyways, I put 'All of the above', because it's mixed.
Like a lot of genres FPS is broad, there's a huge difference between some types of FPS games and others. While some make great hoard/survival games others have amazing campaigns, then we have games like CoD/CS that are basically only for multiplayer despite CoD still having the other modes. Because of this I don't seek out an FPS games for one particular mode, I seek it out for simply being a good game and having at least one of those modes stand out well.
Typically with FPS games however I do expect a Multiplayer and would probably question buying the game if it didn't but if it is strong in other modes I'd still probably get it.
According to TT I have 17 FPS games (gosh, I didn't realise it was that many lol)
None of them actually stand out that much looking at them haha, Payday 2, Doom 3 BFG Edition and Duke Nukem 3D are probably the most positive stand-out games (and 2 of those are old-school FPS), the Call of Duty series is obviously there up until Black Ops 2, I played for multiplayer back in the day, I even used to be quite 'in' with the community. Black Ops 2 however was really just for the Zombies mode. Killzone 2 & 3 were mostly for the Campaign to be honest, although I loved Killzone 2 Multiplayer, they kinda changed it a lot in 3 so... bleh. Battlefield 3 was a choice I made solely for Multiplayer and I almost always had a squad of mates to play with, it really was a blast with friends (I still treasure some of the memories at that time!).
We all serve one master, one king... And his name, is gaming, forever may he reign!