A very good start.
1. I think GTX1060 is appropriate.
Buy an EVGA version. In the event that you find you want something stronger, you can return it within 90days and get credit on a stronger card. A good option that I do not expect you to need.
The one I linked can hold 3 dp connected monitors as well as a 4th via hdmi.
2. The psu you need is gated by the graphics card you use. A GTX1060 needs only a 450w psu.
Even the strongest cards will do fine with 650w.
Here is a chart :
http://www.realhardtechx.com/index_archivos/Page362.htm
Of more importance is the quality of the psu.
Corsair HX is good quality, but 1000w is way overkill.
I might suggest this Seasonic focus 650w unit.
gold rated, modular, 10 year warranty.
https://www.newegg.com/Product/Product.aspx?Item=N82E16817151202
3. I7-8700K is as good as it gets.
stock clock is 3.7 with a turbo up to 4.7
Most will overclock all cores to 4.9.
If price is no object, you can buy a better binned 8700K from silicon lottery that can do 5.2:
https://siliconlottery.com/collections/coffeelake/products/8700k52g
4. You will need a Z370 based motherboard. All are good.
5. You need sufficient ram to hold the contents of all your apps.
Normally, a 2 x 8gb ddr4 kit will do the job, but, I think you would be safest with a 2 x 16gb kit up front.
Speed is not important, something like 3000 to 3600 would be right.
6. A z370 motherboard will hold a m.2 pcie ssd device. A 500gb Samsung 960 evo will have better sequential speeds than a simple sata ssd,
Samsung tends to be a touch faster and be more reliable today.
7. A case mainly needs to hold your parts.
I like one with two front 120/140mm intakes which are filtered.
That will keep your parts cleaner.
Pick one that looks good to you.