theRichieJ :
Thanks for the reply! I am using a capture card to get my gameplay onto a pc, then applying a webcam box and pushing it to twitch. I will also be editing videos on the PC, nothing too crazy, just for youtube. Does that affect that solution you gave me?
That depends entirely on your software and how it renders out everything. If you are going to be doing editing, a faster CPU is generally a good thing.
From what I've seen, most of the cheaper (free) twitch broadcaster programs support QuickSync and NVENC, so Intel is definitely the cheapest way to go. QuickSync reduces video quality a tiny bit, but reduces CPU use for encoding by a massive amount. Perhaps one of the mid-level Core i5 haswell chips (i5 4440/4460, i5 45XX or i5 46XX) by itself would be enough. Just remember to avoid Xeon chips and AMD since those don't have supported video encoders.
You can always add an Nvidia graphics card (950/960) later if you need extra power for editing (most editing software nowadays comes with OpenCL or CUDA for certain functions), but that can wait usually.
Also, if your twitch broadcaster program supports AMD VCE, AMD GPUs are also a viable option, including APU chips like the A10-7850. Fewer programs support VCE than QuickSync though, so I would still recommend Intel for low budget realtime encoding rigs.