The Sennheiser HD 598 are the best headphones I've ever used for gaming. I've gone through a LOT of different headphones and gaming headsets, and nothing touches them. The clarity of sound is amazing, and the sound stage is HUGE which makes them phenomenal for gaming. They are open back though, so something to keep in mind.
For $100 or below headphone+mic solution, there are basically two options in my opinion, through all of my travels:
1. Closed back: Hyperx cloud II
2. Open back: shp9500 & v-moda boom pro
The cloud II are a rebrand of one of the best headphones under $150, while the shp9500 are the value King of all eternity. You can find the 9500s new for $50 US and they sound as good as headphones that cost $200. I've owned several more expensive headphones that are put to shame by these babies. Incredible comfort too.
If you need closed back all in one solution and a budget of $100 or less, buy the cloud II and be done. They are probably still my favorite headphone that I own despite having ones over twice the price. They are extremely fun to listen to and have great imaging. Anyone who buys them as a gaming headset just entered into beginner audiophile territory.
For wireless, I recently got a pair of cloud flights and they are great. They are the best sounding wireless headphones I've ever used, about 90% as good as the cloud II sound wise but no wires. Very comfy too . Only work on pc and ps4 though, no Xbox it switch. Because they sound so similar to the cloud 2, and since I don't need wireless really I will likely return or sell them . Still can recommend them fully.