I can't think of a reason an HP Microserver (about £120-150 with cashback or on ebay) + Freenas wouldn't work best! Bung in any number of hard drives you like (up to 4) and pop in your flash drive (there's even an internal USB port behind the door you opened to fit the hard drives).
Faster, more flexible and cheaper than most dedicated NAS anyway! Gen8 is best if you can find a deal, a very beefy haswell Celeron inside, but they're all foot cubed silent PC's with upgrade options. That flexibility means, if you don't like Freenas (which emulates the fullest featured of NAS boxes pretty well, only with more powerful ZFS tech under the hood) you can always change to nas4free, unraid, amahi, openfiler, openmediavault or anything else - even dust off a copy of windows home server! If you really really really want the full NAS experience you can even whack "xpenology" on there, which is a port of the Synology operating system as used in their NAS boxes.