The difference between LTS and the roiling versions is LTS means you will continue to get upgrades for the 12 tree, If you use the non LTS, then you are expected to just upgrade to the new versions as they come along. neither will leave you with nowhere to go. The LTS is great for servers and static installations that are meant to run for years, for a desktop its not that big a deal either way.
Both the distributions you mentioned are Debian based, so its more a matter of taste. Installs are quick and simple, so why not try all three and use what you prefer.
If you are going to be using it for music playback only, then my choice would be Voyage MPD - very lean install and designed purely for music playback. Can be controlled by a smart phone or tablet with the MPD apps, which are available for both iOS and Android platforms. Keith here uses MPD and I have yet to read about anyone who does not like it. Can be a little tricky to set up if you are unfamiliar with Linux, as I does not have a GUI. But there are plenty of places to get help, especially on the CA forum and don't forget Google
Ubuntu studio is way overkill for just listening to files, Solydxk looks ok but if you're going for a Debian derived distro (which is always my preference) then just get Debian and dress it up from there to do what you want (with what ever window manager / gui you want etc).
I really like Crunchbang for a lean, clean Debian install with a nice aesthetic. (although you should be aware that if you're coming from the windows gui you might find 'openbox' (the default gui in crunchbang) a bit of a surprise) I've set it up to work with Spotify, Madsonic (a streaming server that pipes my music to me across the internet) and MPD with GMPC as a controller / interface for my flac collection.