I would recommend setting up a bare-bones Ubuntu server with samba (or some other file-sharing protocol) and a software RAID 10 setup.
You can cram in as many drives as your hardware can take, and it will be lightning fast.
Security can be implemented in tons of different ways (it is Linux after all)
A few things to note:
SETUP: Getting this setup will require lots of elbow grease and a bit of Linux know-how. It will be worth it. The customization and support that comes from doing something like this is invaluable.
DRIVES: I say software RAID 10 because that can be setup independently from the actual Ubuntu installation - you can boot from a single SSD and mount the entire RAID 10 from inside Ubuntu. The RAID also can be changed without having to reinstall Ubuntu or worry about the installation itself mingling with the data. Basically the OS and the DATA are kept separate.
EXPANTION: Expanding the storage will be a pain (not impossible, but time-consuming) - go big or go home from the beginning with your RAID drive sizes.
TWEAKS: Any tweaks you want to do to increase speed, reliability, etc. can be done by simply SSHing into the server and popping up an internet tutorial (with permission from le boss of course)
BACKUPS: RAID 10 effectively backs itself up, however, there are tons (and I mean TONS) of ways to have your server automatically back itself up to an external source (a SECOND very large server with another RAID 10 setup for example). There is tons of software support (some are even natively implemented with Ubuntu (desktop)) for this kind of thing.
If you want to use the native Ubuntu backup program, I suggest fully installing Ubuntu (desktop, not server. The difference is in the extra-nes). That way you get a ton of super fun tools, and you can easily strip it down to what you need by uninstalling things like LibreOffice. Its a matter of personal preference.
HARDWARE: Hardware matters. A LOT. That means you need power where it counts (for a NAS):
CPU: If you want more than 3 people *sarcasm* pushing files at a time, more cores will be important (look into intel's Xeon linup)
NETWORK: Gigabit isn't even a question. You need it. A capable router (might be overkill), network card (just google "gigabit card". 10 gigabit for super future proofing and bandwidth if you really want it), and cables are necessary.
DRIVES: The drives don't need to be insane. They do need to be good however, and a SATA3 connection to them is needed. I would recommend these for a NAS that operates all day. They're made to be on all the time.
If you don't want to do anything of that sort, then I'd just buy a couple of identical NASs and tell them to back themselves up. Yeah.