Debian – How to run scripts on headless startup

You could use su[YourUserName]-c /usr/bin/vncserver to run the vncserver as user, not as root.

Another point: In your script, there's no difference between starting and stopping the VNC server. Usually, a init script would use different cases to start/stop the service:

case "$1" in
    start)
    # code to start the application
    ;;

    stop)
    # code to stop the application
    ;;

    restart)
    $0 stop
    $0 start
    ;;
esac

Here's an elaborated example how to start a vnc server using an init script.

At the time that this answer was first written, Debian (as installed by default) used "SysV" rc scripts with the start-stop-daemon binary. There was an example script, in the file /etc/init.d/skeleton, that one could as a base for one's rc script. Once one had one's rc script and it was marked as executable, the update-rc.d command could be used to add it to desired run levels.

As the years have gone by, things have changed. In 2014, in particular, two things changed:

• The /etc/init.d/skeleton script was superseded by the example script in the init-d-script(5) manual page, which later in 2018 became the only available base when /etc/init.d/skeleton was done away with completely. The content of the skeleton also changed significantly, no longer needing people to write calls to start-stop-daemon or indeed to write much more than some variable assignments. (See https://unix.stackexchange.com/a/480897/5132 .)
• The installed default changed to systemd, and one instead had to write systemd service unit files (which did not have to be marked executable) and enable them with systemctl enable. There was no example unit file, though. (See https://github.com/systemd/systemd/issues/10572 .)

So as of 2018 you need to write a systemd service unit file that (at the very least) names your script (using an absolute pathname) in an ExecStart setting. You might be wanting, although the question does not specify one way or another, to use a User setting to have the script run under the aegis of your user account and not the superuser's. And you might, again depending from things not specified in the question, need to coördinate the relative order of invoking your script and the (auto)mounting of your home directory if it is separately mounted.