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.
Part of the challenge of timing everything has to do with the flexibility of the music - my husband is the conductor and, in the heat of the moment, he may stretch or tighten up a phrase as it goes by. It's better for ME to follow him with controlling the slides progression than it is for HIM to have to be a slave to the slides' timing.