missed the part about the hardware...
I'd go with a full-on PC, because it's only marginally more expensive than a NAS, and it doesn't suffer from a NAS's limitations and bugs, though it does require a bit more setup, especially because given the price of Windows licenses, you should probably go Linux.
You can find Atom motherboards with 4xSATA for $70. Add an enclosure, PSU, RAM, you're at $150 (HP sometimes have good deals on their ProLiant MicroServer). Then you need disks: add up all your data, multiply it by 2 for starters, and keep in ming you'll quickly be at x4.. a single 4TB disk leaves you with a lot more room for further expansions than 2x2TB, especially since performance is not a concern (so, no RAID).
Someone should buy an extra USB enclosure and fill it with disks for backups, to be done weekly and then disconnected and hidden away.