Budget for the monitor would really depend on what you want. If you want GSync. You'll have to add a few hundred so the monitor Hz are in sync with FPS on the video card. Which is why I went with the Radeon Rx 580 8GB. As it works with Freesync a much cheaper monitor alternative. I'd rather FPS and Hz be in sync rather than higher FPS with the potential for tearing. I prefer IPS panels.
There is also resolution to consider. 1920x1080 or 2560x1440? Perhaps you want to go ultrawide with 2560x1080. The higher the resolution the higher the monitor cost and the higher the GPU cost. Although 2560x1080 is a lower resolution than 2560x1440 the panels are generally larger and they are produced in lower volumes. Both of which adds to cost.
If you want wider viewing angles, richer colors and higher contrast. You'll need an IPS panel. I prefer IPS.
Here is a breakdown. This is assuming a good monitor brand like ASUS or LG. Not a low quality brand like AOC or Acer nor some unknown brand. New prices not refurbished. If you go without Freesync or GSync you can buy them for less.
Freesync 1920x1080 144hz ~$300
GSync 1920x1080 144Hz ~$450
Freesync 2560x1440 144Hz ~$500
GSync 2560x1440 144hz ~$600
Freesync 2560x1440 144hz IPS ~$550
GSync 2560x1440 144Hz IPS ~$800
Freesync 2560x1080 144hz IPS ~$600
GSync 2560x1080 144hz ~$900
GSync 2560x1080 144Hz IPS ~$1,000
Just keep in mind for syncing technology. GSync = NVidia GeForce, Freesync = AMD Radeon. Make sure any monitor you buy has DisplayPort to avoid refresh rate issues.
Given your budget. You'll likely want to opt for 1920x1080 144hz. Personally, I'd go with the Radeon Rx 580 + Freesync. That SSD is a high speed NVMe model. It will make a huge difference in how fast your computer feels. Game load times will be shortened by a wide margin. There is no way I would go back to a hard drive for games. The difference is astounding. The Rx 580 will deliver great game quality. You can drop the detail settings slightly to get the same performance as the GTX 1070 gets at slightly higher detail settings.
If you really want the GTX 1070. I'd urge you to stretch your budget if that is possible to keep the SSD. At least compromise with a SATA 500GB SSD. Not the same level of performance as the NVMe I listed but a huge upgrade over a HDD. Plus use the stock CPU heatsink which still achieves decent overclocks. You can always add the Scythe Mugen Max later. Switch Windows Pro to Home.
Is there a special reason for Windows 10 Pro? Unless you need it to join a corporate Domain, Bitlocker, Remote Desktop or Group Policy Editor. There isn't any reason to get that over Home. It's not like it will add performance to anything. Which would save you $40.
http://gadgets.ndtv.com/laptops/features/windows-10-home-vs-windows-10-pro-whats-the-difference-and-which-one-if-for-you-718532
You don't need a DVD drive to install Windows. As long as you have a flash drive and the license key. You can download the ISO from Microsoft then use RUFUS to make a UEFI bootable Flash drive.
https://www.microsoft.com/en-us/software-download/windows10
http://www.eightforums.com/tutorials/15458-uefi-bootable-usb-flash-drive-create-windows.html
PCPartPicker part list /
Price breakdown by merchant
CPU: AMD - Ryzen 5 1600 3.2GHz 6-Core Processor ($195.69 @ SuperBiiz)
Motherboard: MSI - B350 TOMAHAWK ATX AM4 Motherboard ($96.98 @ Newegg)
Memory: Corsair - Vengeance LED 16GB (2 x 8GB) DDR4-3000 Memory ($120.60 @ Newegg)
Storage: Crucial - MX300 525GB M.2-2280 Solid State Drive ($155.88 @ OutletPC)
Video Card: EVGA - GeForce GTX 1070 8GB SC Gaming ACX 3.0 Video Card ($409.99 @ Newegg)
Case: NZXT - S340 (Black/Red) ATX Mid Tower Case ($69.99 @ B&H)
Power Supply: EVGA - SuperNOVA G3 650W 80+ Gold Certified Fully-Modular ATX Power Supply ($88.99 @ SuperBiiz)
Operating System: Microsoft - Windows 10 Pro OEM 64-bit ($133.99 @ SuperBiiz)
Monitor: Asus - ROG SWIFT PG248Q 24.0" 1920x1080 180Hz Monitor ($0.00)
Total: $1272.11
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-06-18 15:34 EDT-0400