I think the A8 7600 will work with the RX580 OK.
I've run similar CPUs with similar GPUs pretty well.
I ran an i7-920 with a GTX 1060 and that ran OK and the 920 is slower than the A8 (although it's close)..
Well, using Fortnite as a base then, recommended specs is an i5 2.8ghz, so say for example an i5-6400 clocked at 2.7ghz, the Ryzen 2200g outperforms the i5 accoring to UserBenchmark.
No idea what sort of frames you'll be looking at exactly, but there are some vids on youtube of your build, and for a some people even the ryzen 3 2200g is a bottleneck when playing fortnite.
Id say if you can afford it in a few months, pickup A Ryzen 5 2600 for £150, not a massive jump up in cost but it's definitely way more powerful. otherwise a year down the line you'll find that the Ryzen 3's not cutting it and you'll end up upgrading again anyway!