Alright, sorry for the delay. This is what I put together, but this is also my first attempt at a very quiet build, so I'm sure there is room for improvement.
If you want pure gaming, the Intel 7700k outperforms the Ryzen 7 1700 slightly.
However, the 7700k runs notoriously hot, and in a build aiming for silence, I don't like super hot components. The 1700 will also go a lot farther if more cores/threads are used in games in the coming months/years, and in the mean time, it'll be a great asset if you do any other work (video editing, rendering, streaming, etc). If, however, you want pure-gaming, you should wait for the 8600k/8700k from Intel and grab one of those with a Z370 board. Rumor is those CPUs will release in October, but honestly, we just don't know yet.
The CPU cooler is one of the best and quietest air coolers. Highly recommended.
The motherboard could be swapped out for something else if you want. You could go for something ridiculously large,
such as this E-ATX motherboard, as it would give you a more spread out motherboard which would likely run a bit cooler overall as it would improve some heat dissipation, but I don't think it's necessary.
RAM is stupidly expensive right now. For this price range, aim for 3000 MHz and 2x8 GB or better.
Storage = SSD. Old-school HDDs spin up and therefore make a bit of noise. SSDs = silent. You could very easily add in a second SSD or go for an M.2 form-factor SSD which would result in fewer cables running through your case, which is nice, but what I picked for you is a standard 2.5" SSD.
Your GPU could be whatever you need for your gaming purposes. Without knowing what games you want to play, I figured a 1080 would cover most things, and also seems appropriate given your budget. You could easily warrant upgrading to a 1080 Ti. Regardless of the card, I really think getting a hybrid GPU like this will be the best thing for you noise-wise. You can also undervolt the card a bit (I did this with my 1080 Ti) which resulted in a slight (~2-3%) performance increase
and lower voltage, which means less heat, which means my GPU cooler (also a hybrid) runs a bit slower/quieter.
This power supply is overkill in terms of wattage, but the 750w version of the Silencer Mk III series has a 140 mm fan instead of a 120 mm fan that you find in the <750w versions of the Mk III series. Larger fan = lower RPM = runs quieter. Also, the fan doesn't operate at all when you're using less than 350w from the PSU, so for basic web-browsing/at idle, the fan will be silent.
I added in Windows 10 Pro, but you could go with Home instead and save $30.
Added in 2 more fans. This case already has 3 of these fans, but adding two more will hopefully mean you can run all of them at a lower RPM to achieve the same cooling = less overall noise.
Anyway, input from others would be good on this, I think, but let me know your thoughts or if you have any questions and I'll see what I can do to help! As a side note, this is ~$2,000, so you still have $1,000 more to spend if you so desire. That money could be easily spent on a 1080 Ti, and if you don't want to overclock your 1700, you could get a 1700x or 1800x to get more performance without the need to overclock manually.