I have just built a PC with similar objectives: lotsa processing power while remaining as quiet as possible. This machine is intended as a home office workhorse, while also being my main music source. Not into games though.
As you well know, the noise and processing power are conflicting objectives: the faster you go, the more cooling you're gonna need. Coming from a 10 years old platform, I had only a vague idea of what to expect from the hardware available these days, so I spent weeks researching.
Cooling-wise, I went for my preferred solution being air, with the assumption that if it doesn't work well enough, I'll swap over to a water cooled one. But having just completed the build, I know that I won't ever have to do this: air cooling works well enough for me.
My system is i9 10900K based, which is a power hungry beast. Rated at 125W, it can go up to 250W under load. But paired with the be quiet! Dark Rock Pro 4 air cooler, it hardly ever gets over 50 degrees, and most of the time sits around 30. Fans run slow enough not to be heard at all. Only under extreme load there's a low level hum from the case fans.
The case is a biiig one: be quiet! Dark Base Pro 900 rev 2. I went for it for several reasons:
- large cases accommodate more fans and larger coolers if need be, and allow less obstructed air flow. This one comes with 3 x 14cm good quality fans, and I added 2 more. They all run at very low revs, but still provide enough airflow to effectively cool down the box
- since I intend to use a fanless graphics card (still in transit), I want it to sit above the CPU, not below, to enable better convectional cooling of the lot. This case allows you to swap the motherboard mounting plate from the right side to the left, while turning the MB upside down. So the GPU will sit near the top of the case, and right below a case exhaust fan.
- I just like the way it looks, the quality and flexibility of this box
As @xr1st1anos above mentioned, some of the better PSUs run with the fan off until they reach certain level of load. I went with the Corsair HX850W which is platinum rated and doesn't turn the fan on until 40% of the load is reached - in my case thiss means hardly ever (the GPU draws < 75W).