It's not that you can't use the 8350 (my backup is still a 8150 and a 770 which have been doing just fine), but if I were building a new rig I would go with an Intel build. Better performance vs power consumption without having to overclock. If you can make room in your budget to afford the 6th gen CPU skus, it's probably worth doing to extend the life of this system. I am more of an Nvidia fan, but cost vs performance you're probably better off with that 390. That 960 is close to the performance of the 770 I am using and it's handling everything I throw at it with a grin.
You have to decide whether you want to spend the money once and live with it for awhile (my philosophy) or buy what you need now and upgrade as you go.