Usually these kinds of threads make me cringe, and rightfully so for the stuff people recommend. But here’s my two cents: Stop reading anything here that doesn’t have soundstage as a factor. Natural soundstage with an open-back headphone is the most vital thing you could use in most FPS games. Assuming you’re going to be playing something like PUBG, CS:GO, Fortnite or anything of the sort, you’re going to need some headphones that have great width, depth, soundstage and imaging.
The best option that I’ve come to for budget (and even non-budget for people that consider this high-end for choices in headphones, even though it’s really not), are the AD series from AudioTechnica.
YUCK, AUDIOTECHNICA, RIGHT? Wrong. AD series are some of the most accurate headphones (sub $300 I‘d say) you can get for imaging and soundstage + detailed highs and mids. iirc, the higher you go up the better soundstage, vocal presence, and general neutral frequency. I’d recommend these three for you:
AD700X + Modmic (mute switch and newer version): $172
AD900X + Modmic (non mute switch, older version): $198 (best bet)
AD900X + Modmic (mute switch and newer version): $218
The newer Modmic sounds better, by the way, as the old one is generally more nasally and doesn’t have as good of a freq response, plus the mute switch for convenience.
For gaming, you can’t beat these. They’re also pretty good for music if you want accuracy, but I wouldn’t find these enjoyable for listening to music since they’re just too bass-lite for me. Amazon prices below as of 10/27/17.
If you’re doing any other type of gaming (non-shooters) by the way, forget everything I just said and just get something like SHP9500 with a V-Moda since you don’t need spatial positioning.