The other thing I'm going to need to be able to do is to control the rate at which the pictures come up on the display - that is to say, I'm going to be sitting in the control booth timing the pictures to go along with the music performance.
There are a few ways to do an interactive slideshow.
The iDVD webpage says it can create a DVD slideshow in "kiosk" mode with forward and back buttons. But it would better to not have those buttons on the screen.
If your video projector has VGA, DVI or HDMI connector, the Mac mini could connect directly to the projector and display an iPhoto slideshow with music from iTunes. I believe you could use the arrow keys on the keyboard to advance to the next slide, but I'll have to check that.
Another direct-connection option is the built-in FrontRow photo presentation.
Yet another direct-connection option - Apple sells a $80 software package called iWork, which includes Keynote. Steve Jobs uses for his live presentations. This would be the ideal way to go if you need an interactive slide presentation - and it exchange files with PowerPoint. (iWork also includes a word processor called Pages - so it's a good value.)
The latest Mac minis include a handheld remote control - and I believe it works with some of the software like FrontRow and Keynote, but I haven't tried it myself.
The Mac mini includes a 30-trial for both Keynote and Microsoft Office (including PowerPoint), so you could possibly use them for your project before they expire.