I have the PS Pulse Elite headset
It has a mute button though I never used it
I'm not sure but I think that just mutes myself so others can't hear me
But you can adjust the sound of the players and adjust the sound of the game, making the players speak quieter and making the game louder..you can also adjust the bass, and toggle between different noise modes..like sports, cinema, game, etc.
But It might be over your 100$ budget
Unless they came down in price
I paid about 130$ 2years ago for it
Works with all my devices..ps3, ps4, ps vita and my laptop