If you're just storing media (no total disaster if the disk dies), I'd go with an 8TB drive in a usb3.1 enclosure or something similar. You can get two, and mirror them with some form of software raid, or backup one to the other.
Eg something like:
https://www.amazon.com/Seagate-Expansion-Desktop-External-ST...
Or something like this:
https://www.amazon.com/Mediasonic-Bay-Dock-2-5-SATA/dp/B0078...
With a couple of:
https://www.amazon.com/Seagate-Ironwolf-3-5-Inch-Internal-ST...
(Note that 8 and 6 are ~equal/gb, the 10tb version is at a bit of a premium).
Benefit of these docks is it's easy to just have a "backup" disk that you drop in from time to time and sync to, and then you can keep that drive in a fireproof box, or off-site. The down side is that I'm sure the odds of physical drive failure goes up when it's so easy to move the drives around all the time...
If you want "high performance", it's going to be a bit more expensive -- I'd try and pick up a cheap HP Gen8 mini server[1] or something similar from Dell - anything that supports ECC ram and a few 3.5 drives. Install a ~512GB SSD, and set up freeNas/openSolaris/Ubuntu with zfs for linux - and use the disks in mirroring or raidz, with journaling on the ssd.
I've yet to build one myself, but it's what I've been mulling over lately. In the short term 6 tb drives might be a bit more affordable, but I'd probably prefer 2x8tb in mirror right now (to be expanded as 10tb drives comes out or with two more 8tb drives as prices come down a bit) - rather than some kind of parity-based raid setup with 3+ 6tb drives.
This still leaves the issue of backup of that 8-16tb of data though.
It might very well be that two 8tb usb 3.1 drives are better - one for "data" one for "backup" with the option of keeping the "backup" drive in a different physical location (say, the office) -- to avoid a single fire eating both drives.
[1] https://www.hpe.com/us/en/product-catalog/servers/proliant-s...
I've seen a series of these being sold off cheap (not sure if it's as a campaign, or as new models are phased in) - and I've basically seen then at ~the price of a "dedicated" nas cabinet for devices with 8gb of ecc ram and no disks.