Adding a class to a menu item where the class name is set in the node
How comfortable are you with code? 

This sounds like a job for hook_preprecess() inside template.php to get the value of drop down field and store it to something like $var['my_class_to_insert']=. Then inside of whatever.tpl.php used for this situation, have &lt;div class='$my_class_to_insert'&gt;Content goes here&lt;/div&gt;. See https://stackoverflow.com/questions/8124089/ for how to get the value of a field in the template.php file. 

The drawbacks to this second approach is that you are coupling functionality to the theme layer and adding to "Drupal's Div Soup."

Or I'd look at two other modules before you open up a code editor. You could try to use logic in the Context Module 


  Context allows you to manage contextual conditions and reactions for
  different portions of your site. You can think of each context as
  representing a "section" of your site. For each context, you can
  choose the conditions that trigger this context to be active and
  choose different aspects of Drupal that should react to this active
  context.


And Rules may help out...


  The Rules module allows site administrators to define conditionally
  executed actions based on occurring events (known as reactive or ECA
  rules). It's a replacement with more features for the trigger module
  in core and the successor of the Drupal 5 workflow-ng module.


Rules and Context also have a world of other modules that add additional pieces of functionality.