I'm using this Razer Kraken X - Multi-Platform Wired Gaming Headset and I can say only good things about it, bought it from amazon and now is on 15£ discount for UK.
Razer Kraken X Ultralight Gaming Headset: 7.1 Surround Sound Capable on PC Only - Lightweight Frame - Bendable Cardioid Microphone - for PC, Xbox, PS4, Nintendo Switch - Matte Black https://www.amazon.in/dp/B07RMBB4HM/ref=cm_sw_r_u_apa_i_bfUNFbY1RRVBA?_encoding=UTF8&psc=1
4.4 k 7.1 surround sound 50 mm drivers
How about the Razer Kraken X?
https://www.amazon.co.uk/dp/B07RMBB4HM/ref=cm_sw_r_cp_apa_glt_fabc_AM56YZ0CYQ5VV9ANTH9Z
Razer Kraken X Wired On Ear Headphones with Mic (Black) Link: https://www.amazon.in/dp/B07RMBB4HM?tag=georiot-in-default-21&th=1&psc=1&ascsubtag=pcg-in-8879423659951414000-21&geniuslink=true
Here's an rx 580 build:https://uk.pcpartpicker.com/list/vtrnk6
ryzen 3 3100
b450 mobo(has wifi)
2x8gb 3600mhz ram
500gb nvme ssd
rx 580 8gb
24" 144hz 1ms monitor
£791.63
If you could spend 100 more pounds you could upgrade the processor to an ryzen 5 3600, which is a 6 core processor, and is currently the best processor by price/performance for ryzen(https://uk.pcpartpicker.com/list/jrWwMc)
Or, if you want more storage, you could grab one of these: https://uk.pcpartpicker.com/product/mwrYcf/seagate-barracuda-computer-2-tb-35-7200rpm-internal-hard-drive-st2000dm008for 50 pounds.
not sure if you wanted a keyboard, mouse, and headset, so I didn't include it. but, if you do want one you should probably grab one of these keyboards: https://uk.pcpartpicker.com/product/2PnG3C/microsoft-keyboard-anb00006
You'll need a decent mouse for fps games though, so you should get something like this:https://uk.pcpartpicker.com/product/KLVD4D/corsair-harpoon-rgb-pro-wired-optical-mouse-ch-9301111-naFor a headset, unless you're willing to spend an additional 50 pounds, i'd say just use earbuds, but if you are, then probably this: https://www.amazon.co.uk/dp/B07RMBB4HM?tag=pcp0f-21&linkCode=ogi&th=1&psc=1
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if you do need all 3 of those, then your budget is a bit too small i think, you'd have to go over by 25 pounds or so, unless you want to sacrifice some gpu performance(very important for fps games, so not recommended):
https://uk.pcpartpicker.com/list/q6dzmg
^this one doesnt have wifi included
tell me if you need help on how to get windows for free(legally of course)