It's really up to you if it suits you in-game or not when it comes to the first question, though for CSGO I use SS Siberia v2 and it's really good for that game, so that's what I'd recommend IF you would decide to buy a gaming headset.
As for the surround sound, if you want it to come with with the headset itself without buying a seperate sound card ( I don't know much about surround sound cards so correct me if I get something wrong ) then you'll have to buy a headset with 7.1 aka surround sound. Though any decent headset with 7.1 would cost quite a lot, 100$/€'ish 7.1 headsets are generally nothing spectacular and for example the siberia v2 doesn't have surround yet it's really good for FPS games ( CSGO mainly, I hear footsteps from really far distances ).
But as I mentioned, it's up to you if the headset suits you or not, don't buy a new one if you don't need it.