Task:

Computer case fan should cool without lots of noise

The worst fans will make lots of noise without blowing any air, or blow a lot of air with lots of noise.   The best ones will move the most airflow with the least noise.  This one has the best airflow noise ratio I could find.  There are several different sizes depending on where you want to put it, so choose accordingly.

You want to have slightly positive pressure inside the case.  That means having slightly more incoming fans than outgoing.  This reduces dust buildup inside the case.  You should be fine though if you just put fans on all the fan slots provided by the case. 

Airflow should typically go from front to back, and from the bottom up so you don't fight heat currents.