I'm not sure what you want - it looks like you want the default case to open the browser - default is the choice of the user.
Question: the user enters the number 3. The case statement will execute the code block for 3.
So, the user's choice gets taken correctly, correct?

If the user enters 67- which is not in the list - then the default case statement will execute. Right?
So what is your your request for default? I do not understand. You could add echo 'none of these' as a choice.
When the user selects 'none', then the case *) statement executes and you get the extra choice:

Code:

*)  echo "La tua scuola non è presente in lista"
    echo "enter your own choice"
    read mychoice
    chromium-browser   "$my_choice"
   ;;
esac

Plus some of your characters render as a British pound sign on my screen: (pound)INTERNET WEBSITE(pound) so I'm not sure what that means in your code....