I would like to know which is the most correct way to make my Debian automatically start up a graphical application once the desktop has been loaded. The app must be started as root.
Create a file in your home dir called
/home/$USER/.config/autostart/my_app.desktop with the following content:
[Desktop Entry] Type=Application Exec=gksudo my_application Hidden=false NoDisplay=false X-GNOME-Autostart-enabled=true Name=my_app Comment=My comment
Then login again.
You should use gksudo to start graphical apps with root rights.