What extra hardware do I have to buy if Mac Mini is my first Apple product?
The only things you absolutely need that isn't already included are:


The monitor that you have already identified.
A keyboard; a Mac specific one would make sense, but any PC USB keyboard will do you just need to be careful to use the right settings as the layout will be subtly different
A pointing device of some sort.  If you are coming from PCs, you may hate Apple mice (I do), but again any PC mouse will work just fine.  Having said that, the Magic Trackpad is fantastic.  I use one on my iMac and do not use a mouse ever on a Mac any more.


Things you don't not need but are highly recommended would include:


A backup drive!  Backup your stuff!  Make it big (2x your internal drive at least) and make it fast (USB 3 or Thunderbolt if you have too much money)


Things which you might fancy but aren't really needed:


A headset/headphones of some sort (iPhones headphones with the 3 pin jack work fine)
An external DVD reader/writer (any brand, USB)
USB cup warmers (any brand)
Novelty stickers (any brand, except Microsoft Plays for sure! and Windows license keys)