MacStadium has some excellent docs that outline connecting to a Mac mini.

SSH

ssh administrator@xxx.xxx.xxx.xxx

VNC

vnc://xxx.xxx.xxx.xxx

Unfortunately VNC is not secure by default. To secure VNC, you need to setup a SSH encrypted tunnel.

ssh -C -N -L 5901:localhost:5900 administrator@xxx.xxx.xxx.xxx

After you’ve setup the SSH tunnel you can connect to your Mac Mini at vnc://localhost:5900.