Decide on whether you're going to game otherwise no point spending £150/$ etc on a, RX 580.
I could tell you your motherboard isn't failing then you'll have been told it isn't
Could be worth trying a reinstall of Windows. You're going to be doing that with a new PC anyway, and it's a free way to rule out hardware issues and improve performance.
As for the SSD, it won't make much difference which you get. The best bang for buck are things like Crucial P1 and that kind of thing, which offer faster speeds than Sata SSDs, while costing about the same as any half decent Sata drive. A really top tier M.2 SSD like the 970 Evo Plus is probably not worth the premium unless you have fairly specific needs.
As for the PSU, that's actually a bit tricky because right now prices and availability are all over the place. If you want something decent quality, look for Seasonic Focus Gold or Corsair TXm as they seem to generally be relatively
available without egregiously inflated pricing.
In general the parts list seems fine to me.
As for the case, a Fractal Focus G is a good budget case. Depends what you're looking for - other than decent thermal performance, at least reasonable dust filtration, and not costing more than it needs to. If you want a quiet case, or a case with loads of room for lots of HDDs, or something black with no Window, or something stuffed with RGB lighting, there are options.
But I do recommend trying to salvage the existing system since it's free and better for the environment, and the method (clean Windows install) is something you're going to have to do anyway with a new system.
A while ago we showed you how to get a Windows 10 ISO for a clean install. Today we'll show how to clean install Windows 10 from beginning to end.