For fans use noctua for best performance with lowest noise, or Artic P12 for bang for the buck low noise performance. And noctua cpu cooler. The d15 or d15s are the two best options, but other noctua models work well too. These are among the quietest available with very high performance.

you should be able to limit fan speeds in the BIOS settings.

in some situations, using a high airflow case can be quieter than a “silent” style case that’s mostly sealed up. This is because in a high airflow case the system can stay cooler with lower speed fans.

for coil whine, it’s most likely the power supply, seasonic budget models often suffer from this. You can get a nice solid PSU like a Corsair RMx (2019 edition) is a very good PSU and has a semi passive fan that only kicks on when when you a certain % of it’s wattage, otherwise the fan stays off. It also does not have coil whine.

Beyond computer parts, you can make sure the null of true mic is aimed at the noise source, use dynamic mics, and get close as practical to the mics.

also you can put the computer outside the recording room.

good info!

you can also put the computer inside a silent case designed to cool properly.

If you could mention what you yourself chose to do in your setup, that would be helpful.  

Put your computer in a different space or room. In my mastering room I have a separate "machine room" where all the noisy computers live but you could use a closet or just another room in your studio.

I use a Mac pro and the fan is near silent. I use SSD's to record and mechanical drives for backup. I find this works very well for me.