Which microphone is compatible with Mac mini?
I have an older mac mini (2009) - and practically everything works out of the box. (and even some mics show up that I wouldn't even have guessed)

Tested: 


line in (no name)
iPhone Headset through headphone plug
Logitech USB Micro
Samsung Bluetooth headset.
Mic of Sony Camcorder through Firewire


So more likely than not - all you get will work.

Suppose there might be troubles with professional audio equipment - but these should have good enough support to find out for you.