I've cut the cost down by a bit while giving you better functionality. The build below will allow for overclocking.
Changes I've made include changing the CPU cooler, finding a cheaper GTX 1060, changing the mobo to allow for some overclocking, finding a cheaper Windows 10, and swapping the Logitech G230 to a G430 (I've had the G430 before and it's really nice). If you worried about the Cryorig H7 cooler not fitting in the case, it should as the maximum height of the Apevia case for coolers is 155mm, while the H7 is 145mm.
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel - Core i5-7600K 3.8GHz Quad-Core Processor ($199.99 @ Amazon)
CPU Cooler: CRYORIG - H7 49.0 CFM CPU Cooler...