It is possible to build a fanless, or nearly fanless case, but it's more costly and you will sacrifice some level of performance depending on your budget. A more practical solution is one with fewer, larger, slower spinning (and therefore quieter) fans. This is what office/quiet computer users and HTPC builders should strive for. Pick out a case with good airflow and preferably 120mm fan slots (instead of 80mm ones). You will get the same/greater airflow with less noise. Chances are it won't be bling, but that's not a main priority when building a "peaceful" PC. HTPC cases will rarely have 120mm fans due to their desktop form factor, so consider purchasing quiet 80mm fans. It's not going to be the most demanding system so heat output will be lower.