Build one yourself instead of buying it. While budget is an important issue, you need to think about an appropriate case, an antec P280 could be a decent option (plenty of room inside, sandwiched panels designed for maximum sound isolation, rubber grommets for the hard drives to minimize vibration transfering onto the chassis), a fanless PSU (since you won't be running discreet graphics on this server) - Seasonic has some excellent models, and, being fanless, they are 100% quiet, and the integrated GPU on select Sandy Bridge CPUs will be more than enough. If you need plenty of storage you can go with an SSD (60Gb should be enough) for the system, and 5.4k rpm "green" drives like the ones from the WD green series. Since you won't be overclocking, you could go for a passive CPU cooler like this one
. If you follow these suggestions, the only noise that the case will generate will come from the hard drives (slow ones like the ones suggested on rubber grommets and in that case should be very, very quiet) and the case itself (you choose how many fans you want to install).