Figure I'd update this thread with what I decided to get. I'll start with the items and links and conclude with reasoning.
Headphones: Beyerdynamics DT990 Pro 250 ohmsBeyerdynamic DT 990 ProBeyerdynamics DT990 Pro 250 ohms
Mic: Antlion ModMic Wireless
Interface: Focusrite Scarlett 2i2
I couldn't find exactly what I wanted in a headset. I slowly started falling into an audiophile rabbit hole, which I never want to go down again.
I have a friend that does music production and occasionally games too. He uses the Beyerdynamic headphones and loves them. He's used everything from top end Turtle Beach to top end Astro and he prefers his studio headphones for games too, so I went to his place, tried them out and fell in love. He definitely wasn't wrong. Also, all of the research I did outside concluded that a good pair of headphones is going to sound better than the most expensive gaming headset.
I wanted a super clear mic and wasn't ready to go from having no wires to two, so I opted for the ModMic Wireless. My friends say I am unbelievably more clear, which I would expect when I spent $120 on it.
I'm powering it all through a Focusrite Scarlett 2i2 interface, which I was apprehensive about, because all of my research said it wouldn't be enough to power the beefy, 250 ohm headphones. I managed to pick up a used one from Guitar Center and its powering the headphones plenty. Since I plan on doing a little music production on the side, the Scarlett 2i2 was the perfect solution to power the headphones and be able to plug a guitar or bass into without dropping even more money on a headphone amp and separate interface.
Overall, I ended up spending more than I wanted (~$350), but the sound quality is an unbelievable improvement over the old PlayStation Platinum headset that I was using, plus I can now track music.