Performance at that price point is going to be around the same as a console right now. Throw in live streaming it going to suffer performance wise. Higher budget would be a wise idea if you want to do it full time, looking at around 30fps, with the settings low to middle range depends on the game.
Question to ask what titles do you play on playing?
League of legends or hearthstone no problem but other games are going to suffer.
Live steaming takes quite a bit of CPU power which can cause performance issues with framerate.
Bit like getting you to drive a car and do a maths exam at the same time, possible but you have to switch between tasks.
APU build with a GPU would be a wise choice you gain quite a bit of performance for the price against a CPU.
Pair the CPU with the GPU, RAM can also help performance wise. [1UP and Toke going to hate me but it the best choice]
Example
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