Headless MacMini

If you have another Mac (10.5 or above) or an iPad or iPhone, you can remote into the Mini and control it as if you were sitting in front of it. There are two steps to get this working. The first step is to configure the Mini to allow screen sharing. Here are instructions if your Mini runs 10.6 (Snow Leopard):

Mac OS X 10.6 Help: Sharing your screen with other computer users

Instructions are similar if your Mini runs 10.7 (Lion):

OS X Lion: Share your screen with other computer users

The second step is controlling the Mini from another Mac:

Mac OS X 10.6 Help: Sharing the screen of another computer

OS X Lion: Share the screen of another computer

If you don't have another Mac, iPad or iPhone (heaven forbid), but you have a Windows computer, you can use VNC software. You still need to configure screen sharing on the Mini (first step above). Then, you need to get the VNC software on your Windows computer and configure it. Here are some good options:

http://www.wyse.com/products/software/mobility/PocketCloud
http://www.tightvnc.com
http://www.realvnc.com

I hope this helps!

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.

Do I need to download an app to my iphone to control the mac mini with the phone?

Yes. I recommend PocketCloud which is free. It's easy to set up and is very secure.