My past two desktop PCs have been built using quiet components. The older one (which my son now uses) was a fractal design R4 case and is now about 6 years old. Solid build and nothing has broken or fallen off over the years.
Latest one is an NZXT case which is now about 3-4 years old. As I used the DVD drawer a lot for burning CDs, the NZXT case is better as it doesn't have a door at the front and also has the USB ports at the side of the case instead of the top which is perfect for under my desk at my left hand side. Well built and virtually silent when running.
For the newer machine I opted for a water cooler for the CPU, just a standard Corsair all in one device that allows near silent running, even at high load. I tried various traditional coolers and fans with the old case, but they did get noisy when the machine had been running hard for a while hence the water cooler for the new build.
The other thing I added for the more a PSU where the fan doesn't run until the temps go above a certain level. Since I don't do any gaming, a mid spec graphics card with a single small fan that doesn't spin up until really needed completed the build.
The motherboard has fan control built in, and by adapting the profiles, the case fans operate at their lowest rpm until temps go above 55C and then ramp up quite quickly to cool things down quickly.
This means that until the machine has been working hard for a long time, it's virtually silent in operation. We had a friend stay over one night and he didn't realise it had been left switched on and running all night!