I’ve had a Shield TV as a Plex server for about six months. Media is on a Synology DS414 that I’ve owned ~3 years. Both connected via wired gigabit ethernet.
Works great. On a day-to-day basis I don’t have to touch things. I’m just doing the basics - playing movies & music. No DVR, TV tuners, etc. I’ve about 10TB of movies & music. Movies are Blu-ray & DVD rips and mp4/m4v files processed by Handbrake from my old iTunes library. Music is CD rips & downloads in FLAC/ALAC/MP3.
The Synology does have a learning curve but it is straightforward. It helps if you understand basic networking - assigning a fixed IP address, adding users & permissions, etc. Also the concept of RAID, so you understand why four, 4 TB drives results in 12 TB, not 16 TB, available storage. I’ve no experience w/ QNAP or other NAS vendors, but from what I’ve read online, Synology is considered just as user friendly as the others.
No SMB file sharing problems since last Shield update to v5.2. Note that Shield is limited to SMB 1, so if you go with networked storage be sure it supports SMB 1.
Shield TV auto-mounts the NAS after rebooting the Shield or the NAS. When on Shield v5.1, I occasionally had to re-mount the NAS, but process is straightforward. I made a userid on the NAS just for the Shield TV and it has access to just the folders holding my media. It mounts the same way every time and no worries about accidentally mounting a wrong folder.
I’ve owned one NAS, the DS414, so can’t give comparison vs QNAP/others. However, Synology is easy to maintain. All sys admin is via web interface, which can be accessed remotely (has firewall so can limit to specific IP addresses, etc).
Hardware maintenance obviously requires somebody on-site. I had two disk failures about two years ago. Physically replacing a drive is straightforward and does not require tools. Everything else is via the web GUI.
The DS414 motherboard failed about a year ago, requiring replacement of the entire unit. Troubleshooting with Synology was straightforward, but did need somebody to touch the unit - steps such as removing drives, rebooting device, observing status lights, connecting direct to a laptop instead of via a Ethernet switch.
Installing the replacement unit was straightforward, but would need somebody on-site to interact with the unit. The replacement arrived with out of date software (it is a 2014 model). I had to boot with a spare hard drive and upgrade to current version of software. The download & upgrade is straightforward & via web browser, but would be difficult to perform remotely (DHCP address instead of fixed, etc). After the upgrade everything was easy. Power down, put original drives back in unit, power on. Done.
Synology supports backup to local USB drives, remote NAS units and to the cloud. I backup to two USB drives. It runs as scheduled. Restoring is straightforward. Backups to Amazon Cloud Drive has issues, but they are ACD related. That will be going away anyhow due to ACD pricing change in the US. No experience backing up to “real” backup destinations such as Rackspace, Amazon Glacier, etc.
In summary, Shield TV + Synology NAS has been great for me. I would much rather have a NAS than several USB drives attached to a Shield TV. Any NAS maintenance such as s/w upgrades, making new shared folders, etc can be done remotely. Hardware maintenance requires somebody on-site, but that would be the same for any other such device. Synology supports 10 TB drives, so you could load a four drive unit with 4x10TB and have about 30TB of space. Current equivalent of my NAS is DS916+. It supports an expansion chassis to add additional drives. Additional options, both rackmount & desktop, if you want more drive slots. Also, if you do go with Synology, get one with a 64-bit architecture (it is a checkbox on their Product Comparison page). Not strictly needed for Plex. Just future-proofing as some features/enhancements will only be available on models with 64-bit processors.