from your description, wireless hanap mo?
medyo limited lang choices pag gaming wireless headset, tapos need mo bluetooth ang connectivity? that limits it even more
at the top of my head, the cheapest that comes to mind is corsair kaso mga nasa 100 usd yun so its over your budget already (I just checked and its not bluetooth)
there are lots of the cheaper brands (yung mga galing china), you might be able to find a good one (the wired ones retail for about 1k and the wireless ones around 2-3k). but mahirap maghanap ng review so chamba2x nalang pag bili mo kung ok or not