Booting my virtual ubuntu mini as I type. Going to give your light Mate install a try. 
Edit 1:
From a base Ubuntu 16.04 mini VM it was necessary to install the following before the minimum Mate desktop would run
sudo apt install mate-desktop --no-install-recommends
sudo apt install xinit
sudo apt install mate-session-manager
And for some basic functionality
sudo apt install mate-terminal
sudo apt install pluma
So at this point the minimal Mate desktop is running by typing startx at the command line. But wait! No icon support 
To pretty things up a bit
sudo apt install mate-desktop-environment-core
sudo apt install ubuntu-mate-artwork
Now I'm happy 
This is one lean Mate desktop environment. Very nice! 
Edit 2:
To get rid of error seen in both screenshots
sudo apt install mate-applets
This pulled in mate-system-monitor also, but I'm good with that. The VM has grown to just a touch over 2 GB in size.