I would say that your research is correct. MPD is the ducks guts for this sort of thing. (for a full HTPC, i would suggest xbmc, but thats a different kettle of fish).
I use MPD, with a GUI front end, on my desktop, plus I use a web UI, for controlling it remotely via, other computers, tablets, phones etc.
You could easily do away with the GUI, and simply run the webUI.
MPD is the backend, it does the grunt work, the actual playing of the music. There is a list of various clients that act as a frontend, effectively telling MPD what to play.
As far as distrobution goes, it is unlikely to matter. Pick one you feel comfortable with, if you are new to Linux, i would suggest choosing one with good community support (which really, they all have anyway).
You'll need the alsa software packages (Advanced Linux Sound Architecture), mpd, and depending on the client interface, probably a few dependencies for that. Most of the webUI's will require a basic LAMP(webserver) to be set up.