It may sound a stupid question but what Desktop are you using - Gnome,KDE etc?
You say Ubuntu 18.04 is that a true Ubuntu 18.04 or Mate base?
I ask because although Vino is supposed to work out of the box - it doesn't even appear (or work) unless you use the default Gnome desktop which Kstars doesn't like (graphics are u/s ) .Vino-preferences also seems to have gone or hidden.
So
I switched desktop from std Gnome Ubuntu 18.04 to KDE Plasma(can choose which to login too !) and found "Discover" which allowed a simple install and set up of X11VNC Server and Desktop Sharing programs. The latter,Gnome desktop !) does not seem to do anything but X11VNC Server provides a nice simple GUI to configure the service to how you want it to work(See note at the end regarding headless).
used this write up to install KDE Desktop
linuxconfig.org/how-to-install-kde-plasm...-bionic-beaver-linux
Anyway it works, no (well nearly) editing files a simple way to get remote desktop working - see attached screen prints
NOTE Update there is still some manual work to set up permanent passwords (the GUI passwords only stay for a session) and I am yet to test headless)
Without doubt,IMHO, its a mess compared to Windows or RPI Mate/Stretch using Realvnc server - as for the googled junk on VNC its a case of seeing the wood for the tree's
This is a test set up on an AMD 64bit desktop so I dont know for sure it will all work on a Mini
or that everything works 100% but perhaps it maybe of some help.