I am not really fussed over wired or wireless right now.
Obviously wireless would be nice to have but if it comes at 3x the price I'd think twice about that given its simply Bluetooth.
My friend also recommended getting xbox controller as they all have PC compatibility off the bat.
I've seen the PowerA in my searches, that seems like licensed product. Any good?
The Fusion Power A is the best third party controller I've used but still has a USB cable sticking issue, though no a huge deal as it needs the cable by being wired only. Official Xbox one would arguably be the best option but good luck finding a non price gouged one right now, that's why I got the Fusion A as the non gouged next price up option, actually the white version I have is even on sale price. Too heavy for a 5 year old though.
As I said I predict a controller shortage for Xmas, might want to buy while you can. That 2nd OCUK option likely your best bet for best compatibility and at under £30 it's not that bad either.
Though a big UK chain store has plenty of the cheaper Power A wired pads in stock as well, again under £30. Worth looking at those too.
As for Xbox one, seen them gouged up from what should be £45- £50 correct RRP to above £80. Definitely indicative of a shortage as everyone's trying to game during lockdown.