A first PC for my son, done on the cheap, with upgrade options.

My son's been hogging my PC lately, mostly to play indie stuff in my Steam library, but he likes more modern stuff too.

I've inherited an old PC from an in-law which basically needs gutting. The case is decent, and there's a Corsair CX600 PSU in there, almost unused. They did put a new GPU in ages ago, but it's older now, an MSI GTX1060.

My thoughts are this. We don't want to spend a fortune, as I don't know how much he'll take to it, so I don't want to go overboard. My machine is long in the tooth but powerful enough for what I do and what he uses (i5-4570S, RX 570, 12GB), so I was thinking what about a Ryzen APU? Looking at benchmarks, there seems to be plenty kicking out performance similar to my old GPU, and better than the 1060 we've already got in the old box. I thought stick that on a new AM4 motherboard, throw 16GB of whatever (I've not built a new PC in years) in, a decent size SSD. If the CX600 is still good enough, then he'll have something he can upgrade with a dedicated GPU further down the line.

So I guess my questions are:

1. Does this seem like a good way to put together what I want (i.e. not spend much and re-use what I can, but give some upgrade options)?
2. What's the best bang-for-buck way of doing it, in the UK specifically.

All we'll be looking for performance-wise for now is ~60fps 1080p for stuff like Fortnite and the whatever his friends get into. I imagine we'd be looking more like 40ish for more recent games?

I figured I could get something like an MSI mATX motherboard for ~£60, the 3400G for ~£105, 16GB of DDR4 RAM for ~£35 and a 1TB M.2 for ~£40. So sub £300 budget let's say, without a case or PSU if I don't need to.

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Any advice is welcome and appreciated.