The problem is that your x4 860k will hold back that RX 580 to the point where it's not even worth considering.
If you want to actually see how a real bottleneck looks like, adding the RX 580 will beautifully showcase that.
Even at low resolutions and details in modern titles that Athlon will struggle keeping up decent framerates and most likely you'll encounter frame drops, stutters, etc. Adding any decent graphics card will most likely require a platform change unfortunately.
Instead of doing that, I'd suggest upgrading to a Ryzen platform as it's light years ahead of what you have and will actually extract the performance of a RX 580.
So, instead of rushing and buying a GPU, I'll advice you too save some more and build a new Ryzen based system altogether.