ps4 reps confirmed that bluetooth / usb headsets won't be compatible unfortunately at launch, and the few that will won't support chat. they said models that use mixamps / usb-mic + optical sound like astro a40 or a50 will work after an update, but support at the moment for most headsets seems sparse. it kinda sucks, this was my one huge complaint w/ ps4. im sure they'll rollout drivers for BT eventually, but again it's indefinite.
http
![Disenchanted :/ :/](/styles/bom/smilies/disenchanted.gif)
/www.itworld.com/personal-tech/378487/playstation-4-wont-support-usb-bluetooth-headsets-sonys-first-major-ps4-launch-
ps4 will support optical out, so you may have better luck going with an optical headset. the Astro a50 has been confirmed to work but they're a bit over your range. other than that perhaps trittons?
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![Disenchanted :/ :/](/styles/bom/smilies/disenchanted.gif)
/www.headset-ratings.com/astro-a50-wireless-headset-review/
best of luck man. happy gaming!