When I moved 100% to Linux, I could still use all my hardware. There are plenty of vendor-agnostic projects for major brands, like Logitech and Razer. But for me, it was all plug and use.

Most software are just gimmick for lights and equalizers. I have a DAC from soundblaster like that. You can get vendor-agnostic on Linux, like EasyEffects, that offers the same equalizing features, and I can get profiles from other people.

As others said, don't buy "gamming" branded garbage, you can often find the same product cheaper from an audio company, like those Razer microphones (they were good, I have 2 I got from goodwill and both are plug and play).

If you insist on getting gamming junk, some you just need to configure once with their app, and then you can plug it anywere. You might find vendor-agnostic for those.

Audio is very important for gaming, but not all game is made equal. While you can get low latency for visuals, a lot of games use codecs that adds a huge delay in audio. Bluetooth will just make it worse.

A bluetooth headphone, is just a headphone with some extra electronics jammed in there, adding weight and making it harder to fix, and usually more expensive than buying those components apart.

My checklist depends on the hardware and use (gaming, relaxing, production), I am more worried about internal components, how often they break and how easy to fix, but in general:

Headphones:

• Light, for gaming I like extra light. I also prefer open. Both helps with heat/fatigue, and the last to pinpoint things happening in the game.
• Detachable cables, easier to fix. Preferable not proprietary, just because they are cheaper to find extra.

Some people decide on the sound signature based on the games they play most.

I like audio-technica and hifiman entry level headphones, I read some people complaining about recent hifiman. Also, notable IEM : Sennheiser IE 200 (maybe with tape mod).

Mic:

Really depends on what you are recording.

If it is just for gaming, while you are playing and talking with people, do not use a mic on top of your table.
You will just annoy people while typing.

Either use an arm, a headphone mod, or a lavelier.

DAC:

Most motherboards nowadays come with chipset better than entry level DACs. Just make sure they are not branded as "USB interface" as those have huge problems.

Issues like electronic interference are a thing from the past. If you find, avoid that motherboard brand.

If you really need a DAC, check their chipset.

For your case:

If after reading everyone's suggestion, you are still leaning on bluetooth.

Get a wireless DAC with mic, and plug the headphones/IEMs to it.

If the timing is important, do not use bluetooth. If you require bluetooth, do not use other bluetooth equipment nearby, the more devices you add the more latency and loss you have. Also, look into IEM bluetooth, they come with mic, are lighter. Or if you need a headphone, look into wireless DAC.