Thanks for the insights, everyone, especially on pointing out the unreliability of Time Machine to non-Apple network drives. That tip has just saved me a large amount of time and headache!

This is starting to feel like one of those "just pick something" tasks.

Unless I want to build my hardware, you get more bang-for-the-buck with Synology, than with something like the FreeNAS Mini. For example, the diskless Mini has 4 drive bays, 16GB ECC RAM (expandable to 32GB) for $995. For $960, I can get a Synology DS1815+, which is 8 drives (expandable to 18), but only 2GB DDR3 RAM (expandable to 6GB).

Synology pros -- more room for expansion, better form factor
Synology cons -- no ECC RAM, no ZFS

FreeNAS Mini pros -- ECC RAM, ZFS
FreeNAS Mini cons -- no room for expansion.

Beyond that, the capability list between Synology NAS and FreeNAS appears to be pretty much the same.

So, how much does ECC RAM matter? How much does ZFS matter, assuming RAID6 vs RAIDZ2?

At the moment, we probably only have a couple TB of data, so expansion isn't critical at this point. But then aside from the music sitting on the empeg, I haven't ripped any media yet.