How do I keep iTunes from opening on my Mac mini when I plug my iPhone into my Mac mini?

Welcome to the Apple Support Communities!

I understand you would like change the default behavior for iTunes so that it doesn't launch when you plug your iPhone into your Mac mini. To do that, launch iTunes and click iTunes in the Menu bar, then click Preferences. Click on the Device tab and add a checkmark to "Prevent iPods, iPhones, and iPads from syncing automatically."
Sync your iPhone, iPad, or iPod touch with iTunes on your computer using USB
It's possible that the Photos app may launch when you connect your iPhone because it thinks there is a connected camera.
If it does, select your iPhone under the Import tab and uncheck the box "Open Photos for this device."
Enjoy your day!