My Dads PC is old, I remember building it years ago but could not tell you what's in there. If I can bring myself to look tomorrow then I will as I'm assuming there's more cobwebs than parts 
The only thing he uses it for is web browsing (literally browsing the bay and paying bills) and file transfers. He puts films on his portable drive to watch downstairs, but it's very slow.
I figured the main ways to speed it up would be to swap to an m.2 drive, faster RAM 2x8gb 3200MHz or even 2x4gb if I can get away with it, and a motherboard with USB 3.0.
I chose the motherboard because it has 2 fan headers (as well as cpu) since I'd like a case with fans
I chose the CPU with integrated graphics since he won't be gaming on it, but if there's another way around it I'd be interested to hear.
No peripherals needed.
This was before I chose a case, still haven't found one. I need to persuade him to keep the PC on top of the desk as right now it's in a cupboard under the desk so little to no airflow.
He didn't seem keen when I said I could do one for under £400 for what little he uses it for so I thought I'd check with you guys to see if I've gone overkill anywhere or if anyone has any other suggestions, cheers!
My basket at Overclockers UK:

The only thing he uses it for is web browsing (literally browsing the bay and paying bills) and file transfers. He puts films on his portable drive to watch downstairs, but it's very slow.
I figured the main ways to speed it up would be to swap to an m.2 drive, faster RAM 2x8gb 3200MHz or even 2x4gb if I can get away with it, and a motherboard with USB 3.0.
I chose the motherboard because it has 2 fan headers (as well as cpu) since I'd like a case with fans
I chose the CPU with integrated graphics since he won't be gaming on it, but if there's another way around it I'd be interested to hear.
No peripherals needed.
This was before I chose a case, still haven't found one. I need to persuade him to keep the PC on top of the desk as right now it's in a cupboard under the desk so little to no airflow.

He didn't seem keen when I said I could do one for under £400 for what little he uses it for so I thought I'd check with you guys to see if I've gone overkill anywhere or if anyone has any other suggestions, cheers!
My basket at Overclockers UK:
- 1 x Gigabyte B450M-DS3H AMD B450 (Socket AM4) DDR4 Micro-ATX Motherboard= £68.99
- 1 x AMD Ryzen 3 3200G Quad Core 4.0GHz (Socket AM4) APU with RX Vega 8 Graphics - Retail= £119.99
- 1 x Team Group Vulcan TUF Gaming Alliance 16GB (2x8GB) DDR4 PC4-25600C16 3200MHz Dual Channel Kit - Blac= £59.99
- 1 x Corsair TX550M 550W 80 Plus Gold Semi Modular Power Supply (CP-9020133-UK)= £69.95
- 1 x WD Blue 3D NAND 500GB M.2 2280 Solid State Drive (WDS500G2B0B)= £46.99
Total: £376.41 (includes shipping: £10.50)