With my NAS, as with any NETWORK attached storage device, you can not only access it from the internet, but from within your intranet. If your stereo (or HDTV) is connected to your network then you can stream music and HD video wirelessly with a cariety of apps like Subsonic, Plex, etc. I do both. QNAP has two of their own phone apps that I primarily use, Qfile (remote audio and video playback, including transcoding on the fly) and Qmanager (system tools for restart, reboot, etc). As long as I have a cell phone signal I can watch and listen to anything that is on my NAS at home. My box contains 5 x 4TB HGST NAS drives in RAID 6. [Theoretically] With double-parity I can lose two drives and still not lose any data although I have all of my masters backed up in three other places.
One thing to keep in mind about all-in-one boxes like Synology and QNAP is they each use a proprietary OS in their system so no pulling out drives and thinking your gonna read them elsewhere.
You may also want to considering cooking your own with FreeNAS. You can get parts pretty cheap and then upgrade as needed.