Even on the older systems without a CPU fan, there is still noise. The goal, though, is to bring the PC's sound down to or below the standard level of noise of your household. If it is below the regular noise levels, it will not be audible. In specialized environments, though, such as a recording studio, more specialized methods may need to be used. Of course, where real quiet is needed, one may want to just consider a laptop.
Laptops are quieter and are, mostly, just as powerful as their desktop counterparts.
The more wattage your supply will deliver, the more cooling would be necessary, and thus more noise. So, there is no point in putting a heavy-duty supply in a PC with minimal harwdare within. Secondly, you can invest some extra money and get a high-quality supply that produces little noise. You need to check out the user claims on the supplies you look at. Some companies market supplies for lower noise levels, but really they are like a train going by.