I've got a QNAP TS-453 Pro, which has four HD bays filled with 6TB disks in a RAID config. So, after parity I have just under 20TB. This is used for backups of all computers, as well as a virtual server, Squeezebox server (for music) and a few other tasks.
Despite all that, I can still play HD streams without issues via Plex as it has a relatively grunty Intel CPU and RAM. It's quiet, takes up very little space, and works a treat.
Plex is brilliant, but does take a little backend work to make sure all the titles are correctly labelled. You can't mess with their file formats and naming conventions, otherwise the shows just don't show up. But as long as you play by their rules, your video library looks like something you'd see from Netflix - i.e. professional.