Looking for Headphones for Gaming / Music at about 300$

I'm looking for a pair of high quality headphones for primarily gaming and music listening with a little bit of video watching. I'm in the US and I'm looking to spend around 300$. They'll primarily be used at the desktop. In an ideal world, they'd be portable enough for a car ride but it isn't a deal breaker in the end. I tend to listen to a lot of bands like Gunship, The Midnight, Dance with The Dead, but also some more standard bands like Gorillaz and Twenty One Pilots. I'm unsure if I could really get into the audiophile range at that price point (from looking around, I doubt it) but if I could, I'd want the dac and amp in my budget. I have 2 separate questions here.

1. Is it worth my time and effort to save a little more cash and up the budget by a bit
2. If it really isn't worth the time, what would you recommend at this price point