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So so many options on eBay tbh
You'll want at least an 8th gen intel (which will give you native W11 support, you can bodge earlier gens to work though)
Search for a combo of the following:
Dell / HP / Lenovo + SFF
Save budget back to max the RAM and buy yourself some more storage (most only come with 256gb )
Something like this would do:https://www.ebay.co.uk/itm/305409594113
I have one of these (but heavily upgraded) connected to my TV. It's perfect, I would recommend once you find something suitable though search for that model number to see if you can get it cheaper. I only paid £85 for mine.
I've still got a GT 1030 low profile GFX card,(which would fit in the above) spare if you want it for cheap.
A few weeks, I had a saved search. There is 15% off these buyers atm with the code JANJOY15:
https://www.ebay.co.uk/e/coupon-offers/computers-accessories?_kwdomcat=58058&_bkw=sff
Loads of options:
https://www.ebay.co.uk/itm/126267848905
https://www.ebay.co.uk/itm/126275565257
https://www.ebay.co.uk/itm/126266305793
https://www.ebay.co.uk/itm/115710830111