Best single CPU solution for the money is going to be one of Intel's 6c/12t CPUs, the recent 8086k should be great. If you can upload at 6Mbps then you don't need crazy CPU encoding, something like Faster or Fast will do a nice job. And this CPU will have top-end gaming speeds while still being able to encode very well (but not as good as the slower but more-cored alternatives from both Intel and AMD). With Twitch's higher bitrate caps, I think buying the best gaming CPU (fast cores) is a better idea than buying an encoding CPU (lots of slower cores).
As for the GPU, you need a GTX (not GT) class video card for OBS (Nvidia) or the equivalent from AMD.
The rest is up to your budget, which you didn't specify.