Anyone has any ideas on the subject matter? I need to integrate not only regular pages but also webmail, other portals for files and communication etc. on the website.
You can use Drupal, it's flexible to integrate with existing sites. Here is the list of Drupal-based Education Sites
I would suggest you two CMs Joomla and Drupal. Read more about them and choose the the one that best suits your needs.
I've been reading and I can't really make up my mind. I need to make this website thoroughly editable my noobs, so Joomla and Drupal may not be first options, Wordpress is neater. I wish to ask if there is a FILE MANAGER sort of plugin available for Wordpress, where users can easily login and download teacher's notes etc. for their usage right from a Page link etc.