Bakua :
The 8350 would bottleneck the GTX 1080 hard, even with a high overclock. I'd go with an i5 or i7, an i3 would also bottleneck.
Bottleneck hard would be unplayable.
That is completely and utterly not true.
An FX-8350 right now is able to keep up performance wise with any modern AAA title. I still would never recommend buying this processor, and technically yes it is a bottleneck in that the processor will be running at 100% while playing, it won't cause such drops that the system will drag or stutter making the game not playable.
Now that said I wouldn't waste the money on a 1080 for 1080p gaming and recording, the GTX 1080 offers you no advantage, you should run a 1070 it will be closer to the performance of the 8350 and still be WAY more than enough to do whatever you need at 1080p.