Wired is only any use if you do have a sound card as part of your computer's motherboard or as addition.
I suspect the purists will say that wireless must have some sort of added lag. I've used wireless for a while now, my inability wouldn't detect it, and I love the freedom of no wires dangling around my head. I did have a surround sound wired headset and can't tell any difference.
The 7.1 / 5.1 may in part depend on the headset. Many emulate rather than having the multiple speakers needed. Having said that I've only just worked out the added settings in windows and the headphone software (which apparently wasn't running) to get that 3D type sound, yet speakers worked fine.
A lot of headphones say Dolby, but you may pay added licence fees for that.
If wireless you might as well be USB as it's all going to come down to the quality of the amp and stuff in the headset.
Biggest challenge is comfort. And unfortunately buying on line you won't know till they arrive.
Some of the Steelseries are supposed to be a bit different for adjustment with some sort of headband separate to and under the usual over the head padded bracket. Having said that a Steelseries I bought a while ago, and palmed off onto Rammy, was too tight squeezing my ears.
For a while now I've had a Corsair gaming H2100 Wireless which I like, but I got that cheap as a reconditioned offer, and couldn't afford it now.