probably worth explaining the risk vs benefits of buying used and seeing if they are happy to take the risk of used components but have better performance
that way there is no comeback from them if something breaks
"What? I don't remember that conversation"
Oh, just my family?
Personally, I'd suggest they buy from a local PC shop. They'll likely get older and more expensive hardware, but support won't be your problem.
OP: 12100F is a good choice, particularly if you can get a cheap H610 or B660 board when the deals come up. It would be a squeeze to fit in a 6600 at that budget though:
1 X Asus Prime H610M-K D4 - Intel H610 DDR4 Micro ATX Motherboard -
£82.99
1 X PowerColor Radeon RX 6600 HellHound 8GB GDDR6 PCI-Express Graphics Card -
£299.99
1 X AMD RAISE THE GAME - RX 6000 Series Gaming Bundle -
£0.00
1 X WD Blue SN570 500GB SSD NVME M.2 2280 PCIe Gen3 Solid State Drive (WDS500G3B0C) -
£49.99
1 X Team Group Vulcan Z T-Force 16GB (2x8GB) DDR4 PC4-25600C16 3200MHz Dual Channel Kit - Grey -
£49.99
1 X Intel Core i3-12100F 3.30GHz (Alder Lake) Socket LGA1700 Processor - Retail -
£98.99
1 X Phanteks AMP 550W 80 Plus Gold Modular Power Supply -
£64.99
Grand Total: £658.04 (missing case)
You could go for the 10400F, similar price and more choice of boards, e.g. MS B560-A Pro for just over £90. But, would be stuck on a dead platform.