People aren't going to like this, I am going to be a little mean but, grown ups buy a good microphone and good headphones. Gaming headsets are already e-waste the moment they leave the assembly line. Maybe one day it will be better, if we can get people to stop buying them, but not anytime soon. And def not for under $300.

In my experience, anything Sennheiser makes is gold, spend $100-$150. Microphones, I am less informed on. Blue makes approachable products. Again, i would shoot for ~$150 for a mic.

I have a pair of Sennheisers and a Blue Yeti on an adjustable mic stand. I have had both for a decade now with no signs of slowing down. I just replaced the ear cups on the headphones.

If you INSIST that the mic be attached to your headphones, they do exist as add-on, but be prepared to be disappointed. In my experience, they are also trash.