Few things to note;
Ryzen 1700 will hit about the same frame rate, like we're talking so minimal you won't notice;
ALL HDD's make noise but I'd say they're kinda needed. the HDDs I've worked with in the past dependent on where they are in the rig can make more/less noise. The only way to get absolute silence is to have no fans, which is possible but VERY difficult and may require under-clocking your CPU/GPU + a fairly expensive case which can act as a CPU cooler (yes there's a couple of those out there).
Honestly I'd say that running this would be a good shout:
PCPartPicker part list /
Price breakdown by merchant
CPU: AMD - Ryzen 7 1700 3.0GHz 8-Core Processor ($299.44 @ OutletPC)
CPU Cooler: Noctua - NH-D15S 82.5 CFM CPU Cooler ($78.35 @ Newegg)
Motherboard: Asus - PRIME X370-PRO ATX AM4 Motherboard ($141.98 @ Newegg)
Memory: Corsair - Vengeance LPX 16GB (2 x 8GB) DDR4-3000 Memory ($126.99 @ Amazon)
Storage: Samsung - 850 EVO-Series 500GB 2.5" Solid State Drive ($169.99 @ Dell Small Business)
Storage: Seagate - Barracuda 2TB 3.5" 7200RPM Internal Hard Drive ($66.89 @ OutletPC)
Video Card: Gigabyte - GeForce GTX 1080 Ti 11GB Gaming OC 11G Video Card ($683.99 @ SuperBiiz)
Case: Fractal Design - Define C with Window ATX Mid Tower Case ($82.99 @ SuperBiiz)
Power Supply: SeaSonic - S12II 620W 80+ Bronze Certified ATX Power Supply ($47.78 @ SuperBiiz)
Monitor: ViewSonic - VX2475Smhl-4K 24.0" 3840x2160 60Hz Monitor ($361.99 @ Amazon)
Total: $2060.39
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-06-12 03:43 EDT-0400
Reasons:
Noctua make AMAZING quiet coolers.
1700 is still 40eur cheaper
3000mhz RAM just because everyone recommended it for Ryzen (I've finally let it slide, since the price tag is very simlar).
GPU is cheaper than the strix by QUITE A BIT
I've tried to include a slightly larger SSD just so you don't have to use the HDD as much but I'd still suggest getting an HDD unless you wanna spend serious $$ on a SSD set up.
PSU is seasonic silent range so you're all gucci.
Still kept the 4k monitor if you have to go 4k, still recommend against. (coming from a 4k user).