You’ll be needing a working remote access from the outside to your Plex server.
I recommend you to install the Plex server onto your computer first, to try out Plex in general. This can be done for free.
Later, when you have verified that your internet connection is able to support remote access, you can move to a NAS device.
Then you can also consider getting a Plex Pass, which grants you access to the Plexamp app, which is built with music-only in mind.
If your only concerned about music, you really don’t need a NAS device. Now of days the drives in computers should be big enough to store large amounts of music and you can easily add a cloud backup for your music if that is needed.
Install the Plex server on a computer that is on all the time with enough storage for your music library or add an eternal drive for that. Music does not require a lot of bandwidth so unless you have dialup their should not be a problem with that. Just make sure that the remote access is enabled and working.
You have to pay for the android app if you don’t have a Plex Pass which I believe is 5 dollars.