Probably the easiest approach would be:
-> Existing computer with hard drive space in another room
-> wireless 802.11b/g router
-> Apple Airport Express with USB out (or similar device) in your audio room
->USB-to-I2S capable DAC
You can run iTunes, SlimServer or some other the streaming server software on the computer and control it with a something like TelCanto running on an 802.11b/g capable PDA.
You could still build a silent PC for the listening room with a separately located NAS, but if you have an existing PC with some hard drive space available, the above approach would probably be a cheaper way to start. You can always build the silent PC and add a NAS later.
Note that I haven't tried this approach yet myself, so I've probably unintentionally glossed over a few details. If I could figure out an inexpensive way to address HT needs at the same time, I'd be thrilled. As far as I can tell, the best bet for that is a receiver modded to convert a S/PDIF connection to USB(I2S).