I do not think I would pick any of the parts you listed.
Nothing wrong with the motherboard, ram and GTX1070.
With your budget, I would spend a bit more for a I7-7700K or, if you will overclock, a I5-7600K.
A GTX1070 needs a quality 500w psu.
Buy only a good quality unit, preferably tier 1 or 2 from a list such as this:
http://www.tomshardware.com/forum/id-2547993/psu-tier-list.html
Either I5-7600K or I7-7700K will run perfectly well with a air cooler.
A tower type with a 120 or 140mm fan will be fine, and are not expensive.
Buy a nice case up front, you will keep it for a long time.
If it has at least two front 120mm intakes or better, you will have great cooling.