USB keyboard and USB mouse with Mac mini
Apple's Mac mini is the "budget" line of computers and actually does not come with a mouse and keyboard and instead, Apple tells you to "bring your own".

From the current (2017) product page on Apple.com:


  Mac mini is an affordable powerhouse that packs the entire Mac
  experience into a 7.7-inch-square frame. Just connect your own
  display, keyboard, and mouse, and you’re ready to make big things
  happen.


Nowhere on Apple's site does it state that it "only works with wireless keyboards."

Going all the way to the other end of the timeline, MacWorld.com has an article from 2005 that reviews the Mac mini.  In it, it states:


  Apple touts the Mac mini as being compatible with any USB keyboard...


If you cannot use a USB mouse and/or keyboard on your Mac mini, it's time to do some diagnostics to see if those USB ports are functional.