Virtuoso Pro Open Back Streaming Gaming Headset Carbon

You're welcome to DM and I can link you a spreadsheet I manage with plenty of headphones. Most gaming headsets are very overpriced for their sound quality but there are a few that are good value if you buy used or wait for a sale. The Corsair Virtuoso Pro or PC38X come to mind and both eq really well for music.  For standard headphones I'd take a look at the Sennheiser HD 560 or 599. The AKG K7 series are also good for gaming and fairly affordable second hand, not so much new. Then if you want a closed back option there's the DT 770 Pro X. It has excellent imaging and is built like a tank.  As far as a dac/amp goes, you need a DAC if you're hearing any noise or distortion in your sound, if it's not clear. You need an amp if you're headphones aren't getting a good amount louder than your preferred listening level. There's pretty cheap and good dongle options out there. 

I was in the same situation, and I pick a Corsair virtuoso pro. Very accurate sound for music and so spacial sound due his open back design. And still budget. I pick this model about his integrated mic If you don't want mic, I also own a Sennheiser hd560s open back. This two are mi recommendations.

An open-back gaming headset? Good luck finding those, I can only think of a few and all of those are quite expensive. Closed-back headsets are no problem, and some open-back headphones are also doable. Forgoing open-back and going with a gaming headset, I'd say HyperX Cloud III. Forgoing a microphone but going with open-back headphones, I'd say Samson SR850. And if you are willing to spend a bit more without having to buy, say, a ModMic, maybe the Corsair Virtuoso Pro.

Non-planar route, If you want gaming headphones with a mic, corsair virtuoso pro's are actually really nice in my opinion. Graphene drivers, open back, mic isn't as good as the original virtuoso's but still decent. For non "gaming" headphones I'm using dt770 pro's and sennheiser hd600 and love them both.

Corsair HS80 max or virtuoso is my rec Don't get the pulse it has poor build quality and underwhelming battery life

I bought a corsair virtuoso

Never buy a Razer headset. I have the Corsair Virtuoso and it’s been great for me. Wireless but an insane battery life, really good, detachable microphone. Fairly comfortable but not the most, sometimes have to adjust the ear pads.