A lot of home theater or cube or horizontal desktop cases are great for smaller server builds.
That way they fit into component shelves of home entertainment systems.
For silence, you must not neglect cooling at the same time. The best way to do this is to install larger fans at slower speeds. Try to aim for cases that will fit 120mm fans or larger. The best fans have super-quiet bearing systems, and if spun at speeds under 1600 RPM, they're mostly nearly silent. All you get at most is the sound or flowing air thru the PC.
Keep cables tidy and airflow constant and the case will stay cool and quiet for longer, and server uptime will continue.
As for low power consumption, the more you can get integrated into a motherboard, the better, IMO, because you don't have to waste power on something like a video card or sound card. Super-high efficiency power supplies in the under 500watt range are best. Aim for 150 to 200watts higher than your requirements and capacitor aging will not affect the power supply as much over time. Mind you, 90+ efficiency ratings come at quite a cost.
Same goes for super-green storage... there's green platter-based hard drives, and then there's SSDs. Trouble remains to be the price-per-GB on SSDs. Maybe best to wait on those.
Go for the lowest-wattage CPU you can find and you'll save there too.
why use a 125w CPU when you can get an 80w CPU? even less
-install from bootable USBs and avoid even needing a DVDROM drive.
-run it headless and with out keybo/mouse
-use 2.5" laptop drives instead of 3.5" drives and you save oodles of space too!
or just go buy a plug-computer
Myself, I swear by Antec cases. I also really like Corsair PSUs because their warranty is amazing and they ship their PSUs inside a freakin satin bag, in a box! Scythe makes these amazingly quiet S-Flex fans, with fluid-dynamic bearings you can't even hear. Zalman makes very quiet gear too, not quite server-style equipment, but who cares if it performs well.
