cs117x

That would be a great choice. And even Freesync would work with your system as G-Sync.

Not on topic but...
They're pinky and the brain! Yes pinky and the brain!

IMO 32" is way too big for a monitor, and 1080p on a 32" is monitor is a bit low. For 27" and up I'd recommend 1440p.
 
I have 27" 1080p monitor and everything looks big on it because of the low dpi. IMO 23" and 24" are the best sizes for 1080p monitors.

1440p would be the way to go.
 
I have a huge diopter myself.  L +5.25 (and 2 prisms) R +6.25 (and 2 prisms and 0.5 cylinders).
I used a 1080p 32" TV as a monitor on my previous job for a few months. That wasn't good. At that time I had +4 and +4.5.
1080p is the best resolution for a 24" monitor and it can also work nicely on a 27" but above that it's too taxing on the eyes.
1440p on 27" feels a lot like 1080p on 21"-24", simply feels right. And the sharpness is fine.

I have a 27'' 1440p monitor and I'm pretty happy with it

PCPartPicker part list / Price breakdown by merchant
CPU: AMD - Ryzen 3 2200G 3.5 GHz Quad-Core Processor  (£89.98 @ Aria PC) 
Motherboard: ASRock - B450M PRO4 Micro ATX AM4 Motherboard  (£67.19 @ Amazon UK) 
Memory: Team - Vulcan 8 GB (2 x 4 GB) DDR4-3000 Memory  (£60.31 @ CCL Computers) 
Storage: Plextor - M5S Series 256 GB 2.5" Solid State Drive  (£34.68 @ Amazon UK) 
Case: BitFenix - Nova ATX Mid Tower Case  (£29.99 @ Novatech) 
Power Supply: be quiet! - Pure Power 10 500 W 80+ Silver Certified ATX Power Supply  (£59.16 @ More Computers) 
Monitor: AOC - G2590FX 24.5" 1920x1080 144 Hz Monitor  (£187.18 @ PC World Business) 
Keyboard: Gigabyte - FORCE K83 Wired Standard Keyboard  (£43.94 @ CCL Computers) 
Mouse: Corsair - M65 PRO RGB FPS Wired Optical Mouse  (£29.41 @ Amazon UK) 
Total: £601.84
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2019-01-11 11:25 GMT+0000
 
pick up a GPU later on. the iGPU on the 2200G is enough to start with. 
 
also, case is optional if you truly dont care about looks. you can just have the pc on top of the motherboard box with no problems

Buy more RAM later:
PCPartPicker part list / Price breakdown by merchant Type Item Price CPU AMD - Ryzen 3 1200 3.1 GHz Quad-Core Processor £69.00 @ Amazon UK Motherboard ASRock - AB350M Pro4 Micro ATX AM4 Motherboard £65.18 @ More Computers Memory Team - Vulcan 8 GB (2 x 4 GB) DDR4-3000 Memory £60.31 @ CCL Computers Storage Patriot - Burst 120 GB 2.5" Solid State Drive £18.28 @ Novatech Storage Western Digital - Caviar Blue 1 TB 3.5" 7200RPM Internal Hard Drive £36.97 @ Aria PC Video Card PowerColor - Radeon RX 580 8 GB Video Card £184.97 @ Ebuyer Case Cooler Master - MasterBox Q300L MicroATX Mini Tower Case £40.98 @ Novatech Power Supply Cooler Master - MasterWatt 550 W 80+ Bronze Certified Semi-Modular ATX Power Supply £55.40 @ Box Limited Monitor AOC - G2260VWQ6 21.5" 1920x1080 75 Hz Monitor £84.79 @ More Computers   Prices include shipping, taxes, rebates, and discounts     Total £615.88   Generated by PCPartPicker 2019-01-11 11:34 GMT+0000    

PCPartPicker part list: https://uk.pcpartpicker.com/list/n8yBtg
Price breakdown by merchant: https://uk.pcpartpicker.com/list/n8yBtg/by_merchant/
CPU: AMD - Ryzen 3 2200G 3.5 GHz Quad-Core Processor  (£89.98 @ Aria PC) 
Motherboard: MSI - B450M PRO-M2 Micro ATX AM4 Motherboard  (£68.09 @ Box Limited) 
Memory: Corsair - Vengeance LPX 8 GB (2 x 4 GB) DDR4-3000 Memory  (£68.47 @ Scan.co.uk) 
Storage: Kingston - A400 240 GB 2.5" Solid State Drive  (£32.57 @ More Computers) 
Video Card: Sapphire - Radeon RX 570 8 GB NITRO+ Video Card  (£190.79 @ Overclockers.co.uk) 
Case: Fractal Design - Focus G (Black) ATX Mid Tower Case  (£48.30 @ More Computers) 
Power Supply: be quiet! - Pure Power 11 400 W 80+ Gold Certified ATX Power Supply  (£46.98 @ Aria PC) 
Monitor: LG - 24MK400H-B 24.0" 1920x1080 75 Hz Monitor  (£84.99 @ CCL Computers) 
Total: £630.17
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2019-01-11 11:42 GMT+0000
 
Missing Keyboard and mouse but you should be able to get some for £20.
Still £50 above the budget but worth the money in my opinion.
 
Nice deal on the Pure Power 11
2200G will be good for gaming and an upgrade in the future is still possible.
8GB Ram in a budget build is sufficient.
240 GB SSD storage is a bit short to be honest but you can always get a cheap used 1tb hdd on ebay or something.
Solid case 
And the GPU is on 1060 performance and will last several years 

PCPartPicker part list / Price breakdown by merchant
CPU: Intel - Core i3-8100 3.6 GHz Quad-Core Processor  (£114.98 @ Aria PC) 
Motherboard: ASRock - B360M Pro4 Micro ATX LGA1151 Motherboard  (£74.89 @ Overclockers.co.uk) 
Memory: Crucial - Ballistix Sport LT 8 GB (2 x 4 GB) DDR4-2666 Memory  (£58.57 @ Amazon UK) 
Storage: Crucial - BX500 240 GB 2.5" Solid State Drive  (£30.73 @ Aria PC) 
Storage: Western Digital - Caviar Blue 1 TB 3.5" 7200RPM Internal Hard Drive  (£36.97 @ Aria PC) 
Video Card: Sapphire - Radeon RX 570 4 GB PULSE Video Card  (£144.99 @ Ebuyer) 
Case: Cooler Master - MasterBox Lite 3 (Windowless) MicroATX Mini Tower Case  (£38.26 @ CCL Computers) 
Power Supply: SeaSonic - S12II 620 W 80+ Bronze Certified ATX Power Supply  (£56.23 @ CCL Computers) 
Other: Dell keyboard and mouse (£8.00)
Other: Dell 24" monitor (£57.00) https://www.ebay.co.uk/itm/Dell-E2414Hf-24-1920-x-1080-LED-Monitor-with-vga-and-mains-cable/173729770436?hash=item287319ebc4:g:txMAAOSwGIZcNMum:rk:7:pf:0&LH_BIN=1
Total: £620.62
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2019-01-11 12:58 GMT+0000

I would not go Intel at that price point. The AMD lineup under 150 $/£ is just to good price/performance wise. The i3-8100 is 27% more expensive than the 2200G for a 2% performance gain (userbenchmark.com, i know, not absolute and not most accurate). And you can OC the Ryzen 3 a little bit. 
A ok b450/350 Motherboard is still 10 bucks cheaper so over all system cost go further down. The faster ram is also ~10 bucks so it doesn't make a difference at that point.
 
The 40 £ more for the 580 8GB will handle more compared to the 570 4GB especially in new titles in high details if you don't extend 1080p. 
The LG monitor i found is a 75 Hz with freesync. There might be better monitors out there but spec wise it is looking great for that price.

I must have miss clicked. Though I had a 580 in that confic because I just scanned for manufacurer/series and vram 8 GB. 
My bad than. 
Didn't even know there are 8 GB 570s out there in the wild. 

There's literally an RX 580 that goes cheaper than that card, like the one I linked.

PCPartPicker part list / Price breakdown by merchant Type Item Price CPU AMD - Ryzen 5 2400G 3.6 GHz Quad-Core Processor £134.99 @ Aria PC Motherboard MSI - B450M GAMING PLUS Micro ATX AM4 Motherboard £74.95 @ Box Limited Memory G.Skill - Ripjaws V Series 16 GB (2 x 8 GB) DDR4-3000 Memory £110.39 @ Amazon UK Storage Crucial - MX500 500 GB 2.5" Solid State Drive £65.99 @ Amazon UK Case Fractal Design - Focus G (Black) ATX Mid Tower Case £45.98 @ Novatech Power Supply be quiet! - Pure Power 11 400 W 80+ Gold Certified ATX Power Supply £46.98 @ Aria PC Monitor ViewSonic - VX2457-MHD 23.6" 1920x1080 75 Hz Monitor £119.00 @ Amazon UK Keyboard AmazonBasics - KU-0833 +MSU0939 Wired Standard Keyboard w/Optical Mouse     Prices include shipping, taxes, rebates, and discounts     Total £598.28   Generated by PCPartPicker 2019-01-11 11:23 GMT+0000    

yeah I've been suggested this before, I will consider it thank you