For me, SSD is a must have. Normal SSD has 3x the HDD speed while samsung 960 evo has almost 3x the normal SSD speed. It will save your life spent waiting for loading. I valued life more than $130 (https://pcpartpicker.com/products/internal-hard-drive/#t=0&S=460000,10000000&sort=a10&page=1).
But then again its your choice.
Here are my recommendation without hdd, ssd and psu as requested:
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Core i7-7700 3.6GHz Quad-Core Processor ($299.99 @ SuperBiiz)
Motherboard: ASRock B250M-HDV Micro ATX LGA1151 Motherboard ($66.98 @ Newegg)
Memory: Corsair Vengeance LPX 16GB (2 x 8GB) DDR4-3000 Memory ($94.99 @ Newegg)
Video Card: Gigabyte GeForce GTX 1070 8GB Windforce OC Video Card ($379.00 @ Jet)
Case: BitFenix Nova ATX Mid Tower Case ($29.99 @ NCIX US)
Total: $870.95
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-03-15 23:45 EDT-0400
Although its $21 over budget, its has i7-7700 (standard heatsink included), 2x 8Gb DDR4-3000 CL15 (no longer need to add later), GTX 1070. The motherboard B250 should be able to optimized those parts. I think its worth the $21 overbudget.
Good luck with your build