I'm going to go out on a limb and suggest you stay away from "Gaming Headsets" and, instead, go for a combination of a good pair of headphones and something like an AntLion ModMic or a V-Moda BoomPro Mic. I say this because not only is it easy to find a great pair of
real headphones for a lot less money than your average gaming branded headset would cost you, but the overall build and sound quality will be much better as well.
A perfect example of this would be a combination of an
Audio-Technica ATH-M40X (currently on sale for $79.99) and a
V-Moda BoomPro Mic. These particular headphones are designed for DJ & Studio use and they can take a serious beating. It also features a removable cable which makes it a perfect set for the BoomPro because it uses the same connector and this essentially replaces the headphones' original cable. This makes it so it's just a single cable going to his controller, and that's it. While this is not a wireless solution, it gives you something that is far more sturdy and offers much better audio & microphone quality than most, if not all "gaming" branded headsets.
Oh, and he will be able to use this with everything. PS4, XBox, Switch, smart phones, PC, laptop...whatever. Nothing else required.