No persuasion needed. The point of building a pc is that he can get whatever he wants.
Rough sketch:
PCPartPicker part list / Price breakdown by merchant
CPU: AMD - Ryzen 5 1600 3.2GHz 6-Core Processor (£199.99 @ Novatech)
Motherboard: ASRock - AB350M Micro ATX AM4 Motherboard (£64.98 @ Novatech)
Memory: G.Skill - Ripjaws 4 Series 16GB (2 x 8GB) DDR4-2800 Memory (£111.60 @ Kustom PCs)
Storage: SK hynix - SL308 250GB 2.5" Solid State Drive (£73.90 @ Ebuyer)
Storage: Toshiba - X300 4TB 3.5" 7200RPM Internal Hard Drive (£116.74 @ More Computers)
Video Card: Asus - Radeon RX 460 2GB Dual OC Video Card (£71.94 @ Aria PC)
Case: Fractal Design - Core 1100 MicroATX Mini Tower Case (£33.98 @ Novatech)
Power Supply: Corsair - CXM 450W 80+ Bronze Certified Semi-Modular ATX Power Supply (£48.36 @ Ebuyer)
Operating System: Microsoft - Windows 10 Home OEM 64-bit (£83.94 @ Aria PC)
Total: £805.43
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-05-29 19:05 BST+0100
6 cores are nice.
Mobo allows overclocking, stock cooler is good enough for that as well, so if he wants to bump it up a few hundred MHz he can.
Could go for slightly slower = cheaper RAM. Mobo does have 4 slots so capacity upgrades are possible later.
SSD could go for an 850 Evo instead. Slightly more expensive and I wanted to stay within budget.
HDD is a bit tricky. The Toshiba X300 is cheap and basically a rebranded server HDD, so it is fast, but it does make the old school HDD noises on random reads. N300 should be quieter, but so far no reviews to confirm that. Then there's two versions of the Seagate Barracuda Compute. The ST4000DM005 is one of those weird low rpm 1.33TB platter experiments. No idea about performance or reliability. The ST4000DM004 appears to use SMR* and that comes with its own set of problems. WD Blue is also a thing, but definitely the slowest of all options.
There are cheaper GPUs, but mostly low profile and what good is a GPU that could do 2x 4K 60 Hz but doesn't have the connectors for it? DVI-DL = 2560x1600 60 Hz + HDMI 2.0 = 4K 60 Hz + DP 1.4 = 4K 120 Hz (or 240 Hz with compression) so getting both displays to run is pretty much guaranteed.
That case is 44.1 cm x 35.8 cm x 17.5 cm. There are many alternatives and also options to go smaller. Just an example.
There's cheaper options, but nothing modular. Is he willing to deal with the cables?
Went with Windows 10 even though it's shit, but only 8.1 is cheaper on pcp.
*There's some fuckery going on. Some claim it uses PMR, the datasheet says nothing but explicitly states 2 platters (and 4 for the 8 TB version). Also it uses a 256 MB buffer which so far have only appeared on enterprise and SMR drives and that thing sure ain't enterprise at that price. I'm pretty sure it's SMR otherwise Seagate could offer 14 TB PMR and 20 TB SMR drives and they definitely won't do that for a while.
Still some details to work out, but that's the general idea.
I thought I could easily come up with at least a rough idea for both builds this evening but there's a slight problem: Ark: Survival Evolved
Because apparently on epic a 1080 Ti gets you 40 fps. Unless that fits your brother's friend's definition of "good frames" that seems like an unsolvable problem.
By the way, yes, he could get a 1080 Ti.
PCPartPicker part list / Price breakdown by merchant
CPU: AMD - Ryzen 5 1500X 3.5GHz Quad-Core Processor (£166.74 @ Aria PC)
Motherboard: ASRock - AB350M Micro ATX AM4 Motherboard (£64.98 @ Novatech)
Memory: G.Skill - Ripjaws 4 Series 16GB (2 x 8GB) DDR4-2800 Memory (£111.60 @ Kustom PCs)
Storage: Samsung - 850 EVO-Series 250GB 2.5" Solid State Drive (£85.69 @ Amazon UK)
Storage: Seagate - BarraCuda 1TB 3.5" 7200RPM Internal Hard Drive (£37.99 @ Aria PC)
Video Card: MSI - GeForce GTX 1080 Ti 11GB GAMING X Video Card (£659.90 @ Alza)
Case: Cooler Master - N200 MicroATX Mini Tower Case (£43.18 @ Amazon UK)
Power Supply: Corsair - CXM 450W 80+ Bronze Certified Semi-Modular ATX Power Supply (£48.36 @ Ebuyer)
Operating System: Microsoft - Windows 10 Home OEM 64-bit (£83.94 @ Aria PC)
Total: £1302.38
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-05-29 20:18 BST+0100
Again he can pick whatever case he likes.