Get the Sennheiser HD 560s - Gaming. Excellent listening.
Wired. It should be wired.
Removable aka replacable wire. You can solder a wire to repair it, but having a removable one is very nice because there is such a big system for 3.5mm plugs. You can get line extenders, splitters, mic in, mute, etc.
Open vs closed - if you have just one, get IEMs or closed back ones with noise cancelling. For a different listening experience or FPS gaming try open back. The main downside is that now people can hear what you are listening to. The main upside is the sound stage and quality.
Audio Technica ATH 7c - $50 noise cancelling headphones that are great. They would be perfect if they had replacable ear caps. However, they ones included are extremely comfortable. I have used these for 8 hours a day for years. No issues. The pad wore out, but you can sew it back together.
Audio Technica ATX M50X - fun for walking around and base.
Bose QC 25 or 35 - I do not know if you can connect the QC35 wired or if they can only do bluetooth. Either way the ANC on these is great.
Sony XM4 - The only other expensive headphone to consider for ANC.
Apple Airpod Max - They look beautiful, but you will end up throwing them in the garbage because bluetooth only dies. And when it dies you cannot fix it. A broken, torn, damaged, lost cable you can. A bluetooth device that will not charge or will not pair? You can try resetting it, but they are dead.
Sennheiser HD 6XX - These are great, but I chose the other ones because of FPS gaming.
Sennheiser P38X - Supposedly these are fantastic for gaming, AND for music. Why don't I get these? I want removable audio cable and I do not need a microphone. As an all-in-one solution though, these coul dbe good. I prefer to have a separate microphone because of modularity and replacability anre repairability. If I didn't already have other stuff set up, I would consider this one heavily for FPS gaming and music.
FPS gaming and music - HD 560s, P38X
Non-FPS gaming (where position does not matter) and music - HD 6XX or ATH M50x
Only one? - Get closed back, with noise cancelling. The open back options are difficult and IEM or ear buds all the time is not comfortable. Get the ATH 7c with ANC for huge value, get the Bose QC 25/35 or the Sony XM4 if you want to spend premium.
Mainly at home gaming and listening?
HD 560s and IEMs for travel / outside
Alternatively, get a set of ATH M50x if you want closed back
Do you exercise?
Add cheap bluetooth earbuds if you work out with music, travel, etc.
Get a wired, over ear headset with ANC
Alternatively get a set of earbuds if you just do not care. Jabra or something. The issue with earbuds is that they die. But if you only have one and you use them all the time, I understand the use case.