I have a stereo headset with a boom microphone. It uses a 3.5mm jack. I was wondering if I can use the headset and the mic on my PS3 with a USB adapter? What kind would work? Thanks.

no , only certain specially designed stereo headsets are ps3 compatible
it supports any mono usb headset or bluetooth headset , or ps3 specific stereo gaming headsets

you can use any bluetooth or mono usb headset ( must be usb , not using an adapter )
just plug the headset into the usb port and setup in audio device settings or connect it using bluetooth in accessory settings then setup in audio device settings