That's a tough one.
Your system in the main, is pretty beastly (CPU, amount of ram), that's not the issue. The real issue for you is the GTX1060. Although it's a decent 1080p 60hz GPU for gaming alone, when you want to stream too, the card meets it's limitations.
You have to balance in game settings, probably low, to keep a 60hz/fps rate going while you game, so you can output some level of a quality stream. If you don't have a smooth 60hz while gaming, it will really show in the stream. Then you have to consider the stream, and output quality. Because of the GPU being a bit on the light side, choosing anything more than maybe 30fps at 720 as the output would also look pretty bad. It will be stuttery, and not an enjoyable experience to watch.
I'd recommend getting at least a GTX1070 8gb. The extra 2gbs vram really helps, but you also need a GPU capable of hitting 60hz whilst you stream, so that the gaming is decent fps, and the video being watched is of reasonable quality.
It might be just an idea to start with low presets for OBS and low in game settings and see what they look like. Move upward from there if you feel the GPU isn't maxed out.