10 years is a very good innings. What platform you play on might influence this question. I think most around here would probably answer wired over wireless, but obviously that can be very subjective. £50-60 isn't a huge budget, so the wired headsets/headphones in this price range will be limited. Wireless even more so.
I've only had a couple of wireless headphones over the years (I used wired) and from an audio quality POV they were OK. Audio will be compressed to be used over the wireless protocol, even on top of any compression the games use. Wireless is generally simpler not having to potentially worry around a DAC/AMP, or noise/interference from the PC, able to do EQ on the headset (although can be a downside; via the manufacturers software, or app) and no wires. A desktop/separate mic will be much better quality over a headset/boom mic, but cost will increase as will complexity. I think the starting point for these is going to be c.£40-50 for a Fifine USB/XLR mic, but then you would likely want a boom arm on top of that. So more space needed too.
A wired headset/headphone audio quality will be better, don't have to worry about battery life and the headphones can last longer (no battery to replace). Personally I prefer wired headphones/sets, but I already have the DAC/AMPs setup for music and general audio at my desk so it's an easy choice.
You probably have a few choices:
1. Buy a wired headset to replace what you had for £50-60. Cloud 3, RIG R5 Pro, Turtle Beach Atlas 200 - all have reviewed well and mostly in-budget that I know of (might be missing something here - not my area of expertise).
2. Buy wireless, albeit you may have to increase the budget here.
3. Look into headphones, or more expensive 'audiophile' grade headsets. You might want something fairly easy to drive (so low impedance, high sensitivity) that you can plug directly into your PC, or console. This will also open up choices like open-back, or closed-back etc. But may open a can of worms in-terms of if you need a DAC, or AMP etc.
Lot of ways you could go here, so hard to recommend something straight off the bat. Going to a channel like GadgetryTech on Youtube and following one of their headset guides might be a good place to start.