Seeing as though your main use is gaming, I'd look at either the i5-6600k or i7-6700k. Both would perform exactly the same for gaming but the i7 would be a bit better in some of the other work stuff. Considering that and the budget, the i7-6700k is probably best. The above PC looks great but you could get something with similar performance for less cash.
With the RAM, 8GB is more than enough for gaming but considering the other uses of the PC I'd get 16GB now with enough room on the board to easily upgrade to 32GB. I wouldn't spend much extra on faster RAM because it doesn't make much of a difference with Intel CPU's.
With the graphics card, I'd either get something cheap like a superclocked GTX 950 then buy a new card when Pascal comes out later this year or just go for a GTX 980Ti now. Workstation cards would be useless for gaming and the Titan X is horrendously overpriced. It is almost identical to the GTX 980Ti but costs like $500 more.
I wouldn't bother with an M.2. drive personally. You only really notice the performance difference with sustained reads and writes and in those cases they get too hot and just throttle and slow down to SATA speeds anyway. If you do decide to go for one, I'd put it in a PCI-e slot with an adapter and rig a fan to it. If you're willing to do that it will absolutely scream in terms of speed.
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Core i7-6700K 4.0GHz Quad-Core Processor ($334.88 @ NCIX US)
CPU Cooler: Noctua NH-U14S 55.0 CFM CPU Cooler ($69.89 @ OutletPC)
Motherboard: Asus Z170M-PLUS Micro ATX LGA1151 Motherboard ($118.99 @ SuperBiiz)
Memory: G.Skill Ripjaws V Series 16GB (2 x 8GB) DDR4-2133 Memory ($49.50 @ Newegg)
Storage: Samsung 850 EVO-Series 1TB 2.5" Solid State Drive ($309.99 @ Best Buy)
Video Card: MSI GeForce GTX 980 Ti 6GB Video Card ($623.00 @ Amazon)
Case: RAIJINTEK STYX MicroATX Mini Tower Case ($84.99 @ Newegg)
Power Supply: EVGA SuperNOVA P2 750W 80+ Platinum Certified Fully-Modular ATX Power Supply ($115.36 @ Amazon)
Case Fan: Noctua NF-F12 PWM 55.0 CFM 120mm Fan ($19.46 @ Amazon)
Case Fan: Noctua NF-F12 PWM 55.0 CFM 120mm Fan ($19.46 @ Amazon)
Case Fan: Noctua NF-F12 PWM 55.0 CFM 120mm Fan ($19.46 @ Amazon)
Total: $1764.98
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-04-30 08:38 EDT-0400
Not everyone likes that case but I think it looks great and it has a decent cooling design. I'd have 2 x Noctua fans blowing air in through the top, face the CPU cooler so it is blowing towards the bottom of the case and have 1 x Noctua fan exhausting through the bottom and remove the rear Raijintek fan. That would give you excellent cooling and it should stay ultra silent. (The motherboard only has 2 x 4 pin chassis fan connectors so I'd use one of the PWM splitter adapters that come with those case fans to connect both intake fans to the same port on the motherboard.) Then the case and CPU fans will speed up/slow down depending on temperature with a minimum of only 300RPM and the PSU/GPU fans can go to 0RPM.
Performance-wise the cooling should be more than good enough to get a stable 4.6Ghz overclock, it has room to upgrade to 32GB RAM easily and that's one of the best GPU's on the market at the moment so it can play any game on ultra. At 4k you may need to turn the settings down slightly but at 1080P and 1440P it is more than fine.
Let me know if you've got any questions about that.
EDIT: I've noticed the link for that case doesn't work but you should be able to find it for a similar price somewhere. There are windowed and non windowed versions and they come in loads of different colours too.