budget: under $1000
use: playing and streaming minecraft. (without a lot of fps lost in game)
You didn't mention if you need a monitor and all that so assuming you don't, this build will do you just fine for streaming and playing Minecraft.
PCPartPicker part list / Price breakdown by merchant
If you do need all the peripherals. Had to downgrade the GPU to a 1050ti but it was 4GB so I would imagine you'd be fine with that as well. 1060 may be overkill anyways.