I just installed my NH-D15 to cool my R5 1600 and it never went over 65C after 10min of Aida64 @ 4GHz and 1.45V (60C after an hour @ final stable OC of 3925MHz and 1.3875V). It's overkill for most setups but you will never worry about temps or sound and it's super easy to install.
i7 7700k or ryzen 1700 + a GTX 1080 is what I would go with on your budget, however your demands of 60fps on a 1080p doesn't require more than a GTX 1060 or RX 580.
Edit: misread your budget. At that budget I would go with a R5 1600 and a 1060/580.
Cpu: R5 1600 @ 3.8GHz, 1.3125V w. Wraith Spire
Ram: 2x 8GB, 2400MHz
Mobo: MSI B350 Tomahawk
I'm getting a NH-D15 to chase a higher OC. The Ram is taken from the i3 6100 build I used previously, will maybe get faster ram in the future.
When I first booted my MSI B350 TOMAHAWK and 1600 combo the stock voltage was 1.3ish, after flashing to latest bios it was 1.45ish. I immediately took that down to 1.35 then OC'd to 3.8GHz and then lowered the voltage in 0.0125 increments until I was stable at 3.8, 1.3125.
Well maybe, my 1600 maxes out to 73°C @ 3.8GHz and 1.3125V during AIDA64 stability test. I'm happy with this overclock and I'm only buying a NH-D15 to keep the noise to a minimum, not that the Spire is super loud but I want to Handbreak overnight and my desktop is in my bedroom...
Btw. you will have to run the cpu fan at 100% on the Spire over 70°C if overclocking.
Where I'm from (Sweden) you can, and I did just last week, get a R5 1600 + B350 for just a little more than a 7700 and a little less than a 7700k without a mobo to go along with them. The value is definitely on the AMD side and even though gaming performance is slightly better at 1080p on the Intel side you would never see it as you will be GPU bound by that 1050ti (I am too with my 1060 3GB & R5 1600).
The Spire is great. I'm running a lazy OC of 3.8GHz @ 1.35V on my 1600 and temps are 75-77°C during Aida 64 stability test (fan not to loud even at 90% and the sound is pleasant, i.e. not whiny or pulsating).
I will upgrade but only because I need next to silent cooling for overnight video encoding.
Are you already using a Wraith Spire and thinking of upgrading or are you looking for general information about these coolers? If the latter, I am since two days ago using a Ryzen 1600 on a MSI B350 Tomahawk and the Wraith Spire for cooling (for now) and it runs at a moderate OC of 3.8GHz @ 1.35V. It maxes out at 76°C after 40min of Aida64 stability test with the fan running at 90%. That fan-speed might seem high but as many reviewers have said it is actually quite quiet, especially in my FD Define R4 (non window).
The included Wraith Spire CPU-cooler seems to be enough if you don't need to push the OC to much, like keeping it at 3.8 or bellow. As memory speeds is crucial for Ryzen performance I would suggest to double check the MB's RAM compatability.