just put on the best air cooler and a case with good ventilation. However, good air cooler tends to need larger case. My take with that budget with Intel:
PCPartPicker part list / Price breakdown by merchant
CPU: Intel - Core i9-9900K 3.6 GHz 8-Core Processor (£491.98 @ Aria PC)
CPU Cooler...
budget and country?
you should consider AMD Ryzen or Threadripper for that usage. I7-7700k only has 4 cores/8 threads, not enough power imo. I9-9900k is pretty good too but cost is high.
Something for you to consider: https://www.newegg.com/Product/Product.aspx?Item=N82E16834316592&Description=2200u%20laptop&cm_re=2200u_laptop-_-34-316-592-_-Product
add an ssd. 2200U vs I7-6500u
https://cpu.userbenchmark.com/Compare/Intel-Core-i7-6500U-vs-AMD-Ryzen-3-2200U/m36930vsm480281
https://www.gamestop.com/xbox-one/accessories/xbox-one-ear-force-stealth-420x-wireless-headset/124787
saw this review: https://www.reddit.com/r/TurtleBeachHeadsets/comments/7h59qd/low_volume_turtle_beach_600/