I'd recommend Keynote as a fast and easy way to design the presentation with the manual control you need to pace the images to the music - and impressive transition effects for the projected images.
The design process is simple. First, you select one of the basic visual themes for the slides. Then drag your images or videos into the design window in the order you want them presented, and set optional effects like crossfade, page turn, etc.
After your design is completed, you click the play button to start the presentation, then press the space bar to advance to each subsequent slide.
Keynote has a feature that might be useful - but is not available on the Mac mini. If you run the presentation on a MacBook laptop computer, the projector can show the current slide at full size for the audience - but on your computer screen in the projection booth, you can see two slides: the current slide and the next slide. That could make it easier to synchronize your manual control to the music.
In the image below, the MacBook screen on the left shows what you'd see in the control room, and the right screen shows what the audience would see on the projector.
Apple has a video demonstration of Keynote's features here