Not sure if you have spent some time reading through this forum, but there is heaps of information on a lot of great setup options.
You might want to check out this post. (update in progress) Falenkor's Competitive Headphone Write Up. Now with added Hardware explanations! - #670 by Falenkor
It’s geared towards competitive gaming, but there is so much good info on different headphones, and a lot of questions asked like yours that encompass music and gaming.
Some things you’ll want to consider is comfort (clamp force) and if your sensitive to bright sound signatures (treble).
I have the 58x’s running on a G6. I love them for music and for general gaming they are great. Super lightweight. It’s an entry level audiophile setup, but it has been great. With your budget you have quite a few options to choose from.
There are some very informative guys on here, like Falenkor, who will probably chime in and give you some solid options. Good luck!