Headless MacMini

This might be the simplest solution for shut down, but it requires a keyboard. If you press these four keys at the same time (Control-Option-Command-Eject), it will quit all apps and shut down the computer without any more interaction on your part. If you have any unsaved files open (unlikely if you're only using this as a music server), it will give you a chance to save changes.

I do control my mac mini with either an ipod touch or iphone and will try the screen sharing recommendation.
When I first got the mac I tried the VNC route but never got it to work as I'm not the most computer savvy guy. Maybe I'll get my 14-year-old grandson to set it up. ;)

I set mine to automatically shut down at 12:00AM and boot up at 3:00PM everyday. If I want to shut it down earlier, I use a VNC client from my iPad or iPhone to remote control it.

The auto shut down and boot up time can be set in:

System Preferences->Energy Saver->Schedule.

What I do is use some sort of VNC remote viewer software on another computer or an iPad (I use the free Mocha VNC Lite). Or, if you have another Mac use the built-in remote desktop. These solutions require remote access to be enabled on your Mac Mini. Then, just use the Shutdown menu item underneath the Apple menu. A keyboard or mouse isn't necessary for this.

What I do is use some sort of VNC remote viewer software on another computer or an iPad (I use the free Mocha VNC Lite). Or, if you have another Mac use the built-in remote desktop. These solutions require remote access to be enabled on your Mac Mini. Then, just use the Shutdown menu item underneath the Apple menu. A keyboard or mouse isn't necessary for this.