My budget would be $600 and it would need window 10, monitor, and if possible a wifi adapter. I got the keyboard and mouse covered.
pcpartpicker I couldn't really fit in a wifi adaptor as I'm already a bit over budget. I have you a 380 which is better than a 960. A i3 4170 dual core with hyperthreading. This will need to be upgraded at some point though. I have a 750gb hdd and a good power supply with a nice ish case.
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Cheapest really possible especially including the monitor and OS cost. Depending on what games you plan on streaming it may not work so well.