Do NOT in any circumstances go with an FX CPU. Period. This is coming from an AMD fan, but those FX chips compared to the ryzen chips are just not worth it. The performance just isn't as good.
Older Intel i5's and i7's are still decent, but stay away from FX. The build above is good, throw in about 100 for a copy of windows 10.
Another option would be to grab a ryzen 5 2400g and drop the GTX 1050. That should give you better CPU performance, and still give you decent graphics. Not as good as the 1050, but it should allow you to play esports titles like overwatch, etc. However, the good thing is that it would open up your budget to include a copy of windows, and allow you to add a dedicated graphics card later on. If you wanted to save more, you could get the ryzen 3 2200g which would keep your CPU price roughly the same.
So actually if you got the 2200g, add windows, and remove the GTX 1050, that should put you around 475.