Your biggest problem will be finding an ideal case. "Mini-ITX" and "small" don't often go together with "4 3.5-inch drives". There are some nice ones out there, but nice means expensive.
Though I've never used it, you might consider something like the Ark ITX case, $139 on Newegg, or the Lian Li PC-Q25B, $119 on Newegg.
RAID is not redundant. If you want true redundancy, you want to either 1) set up your NAS with an online cloud backup service, 2) buy a couple of external hard drives and have your NAS periodically copy its contents to the drives, or 3) buy a couple external network-capable hard drives (like a WD My Book with Ethernet) and have your NAS periodically rsync to them. Those are your only true redundancy solutions.