Mostly agree with Oko. A home server NAS box doesn't need much CPU power. An Atom is low power (saves quite a few $$$ on electricity), which implies low noise (not so much fan noise), and saves money, and has more than enough oompf to serve files at 50-100 Mbyte/s. I have a 6- or 8-year old 32-bit Atom, and it does fine. With 4Gig of RAM (of which only 3Gig is accessible in 32 bit mode) it has enough memory to run ZFS, and quite a few servers (DNS, DHCP, NFS, CIFS, Apache, ...).
For the case, look for something that is compact and high quality. I ended up with a shoebox-sized Lian-Li case, which has hot-swap disk mounts. Not because I would ever swap them while running (I actually need to unwire it to get it out of the shelf it sits on), but because it makes installing disks easy. The case is also really well built, no sharp edges, sensible hardware to mount the motherboard and extension cards, snap-off covers, good case fan, and such.
For the boot disk, I used some old Intel SSDs that I got a good deal on. I think mine are 32GB in size.
For data disks, definitely go for redundancy. I have two Hitachi 4TB nearline SATA drives (enterprise-grade drives, not the consumer line). The sweet spot in terms of $/GByte is probably around the 8TB drives right now, but few home users actually need that much storage, and smaller drives are actually cheaper in absolute dollars. For file system, ZFS is the best choice, because it gives you built-in RAID, checksums, ease of use (in particular when doing disk replacement); you just have to learn the concepts like "zpool".
In my case, the motherboard choice was forced by needing two Ethernet ports (for firewall), plus a parallel port (I have a 20-year old laser printer that I can't get rid of for emotional reasons). I have no specific recommendation for a motherboard for normal users.
Finally: Get a UPS. It's not very expensive, and small power outages are very annoying if all other computers in the household are laptops, but nobody can get any work done because the server is rebooting.