I would be less worried about streaming content to external parties tbh. They can always sort out their own systems if they want to watch stuff. Plex PASS isn't cheap to maintain.
Get a cheap NAS to hold your storage and run the apps you want, I still recommend Synology personally - it just works, and you can start with fewer disks and add more later if you use SHR (Synology Hybrid Raid). If you don't want to spend that much look at competitor NAS products and what they can do. I suggested the HP microserver (model was included in a previous response) running XPEnology OS if you don't want to spend too much, but it will certainly be more fiddly from your end to set it all up and keep it running the same as a standard Synology NAS.
Sit your NUC next to the NAS on the network, run Plex Media Server from the NUC, point it to the storage on the NAS. the NUC should do a good enough job of transcoding if required.
Get cheaper clients for your TV's to run a dumb Plex Client from, I use RPI2 it works just fine, each one is less than £50 all in, you don't need a NUC to play MKV files or whatever, RPI2 is just fine.
