I had a similar dilema a while ago and went with a NAS – it’s great and sounds like what you want. Quiet, always on, low power.
Mac mini as a music/media server and wireless streaming
Linux Laptop
Windows Laptop
QNAP NAS drive serves files to all of these, plus runs my webserver, iTunes server, downloads torrents, print server and all sorts.
Network transfer speed is usually limited by the CPU in the NAS (despite many claiming Gigabit LAN) so buy as fast as you can justify if you plan on moving large files around between machines.
Also, don’t forget to backup your NAS. Get one that supports USB backup to an external drive.
I back up all machines, phones etc to the NAS, then back up the NAS to an external removable hard drive. For extra paranoia, store a spare one at your work/mates.