
Sennheiser
HD 560S
Budget gaming king with clear sound, but tight fit.

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While 6\*\* series are great headphones, I wouldn't recommend them for gaming. Their pads do wear out over time, which affects the sound. I assume since you'll be using them for long hours, you might not get to enjoy them to the same degree for too long. And replacement pads aren't always available, nor they're cheap. 3rd party replacements are never the same as the originals. You also have the issue of being unable to swap the cable for one with a boom mic. My suggestion would be to go for one of these: HD560s, HD505, HD550 or HD400 Pro and then pair them with HD500 BAM to get the mic functionality, if you need it. Do consider HD490 Pro if you don't need a mic because that's both the most comfortable and the best sounding headphone that I own. You can use them for hours without any issues. Personal tastes differ, of course. Some still prefer the 600 series.
Thanks! Do you have a budget in mind? Sennheiser has a number of comfortable open-backs that are tuned more on the warm side, such as the HD 505 (though I prefer the more neutral HD 550), HD 650, and HD 650. This is probably a good starting point. Comfort on these is pretty good as well (especially the newer models).
They are great. But if you want a more laid-back presentation you could consider the 550, 505, or 599. 560s are kind of bright and analytical. This can be fatiguing for some people.
Sennheiser even sells a boom mic for the 500 series now. I got a pair of 505s and its so nice having the convenience of an attachable mic without having to sacrifice sound quality.
550 is the 505 with better bass and slightly less focused on the midrange. (505 is great, just not what OP is looking for, in all likelihood.)
Other way around; the 505 has the elevated ear gain, at least on my head and the measurement rigs I've seen. But you like what you like!
Fiio FF1 (sadly mic doesn't seem to work - possibly OMTP vs CTIA incompatibility I've not looked into it) or Sennheiser HD505 (sometimes I hook up the Fiio QX13 for a better audio experience). I don't really do wireless personally.

Sennheiser
HD 560S
Budget gaming king with clear sound, but tight fit.

Sony
WH-1000XM4
ANC king, durable, but unreliable mic and touch controls.

Sennheiser
HD 6XX
Legendary mids, durable, but narrow soundstage and weak bass.

Sennheiser
HD 490 PRO
Super comfortable, wide soundstage for gaming, versatile pads.

Sennheiser
HD 599
Super comfortable, easy to drive, wide soundstage, open-back.

Ranked #1
Sennheiser - HD 6XX

Ranked #1
FiiO - FT1 Closed-back Headphones

Ranked #1
Sennheiser - HD 560S

Ranked #1
Sony - MDR-7506

Ranked #1
Sony - WH-1000XM4

Ranked #1
Sennheiser - HD 560S