Whether you go with AMD or Intel, streaming likes more cores.
I recommend an FX 8350 or i7 4790k + 16gb of RAM. And if you can find capture/streaming software that can leverage Intel's QuickSync and HyperThreading that will definitely help with CPU load.
If you decide to do video capture and editing later, you want a dedicated HDD just for that. Keep it clean and don't install to it or use it for anything else. Also turn off indexing for the capture/editing drive.