I'm very experienced at developing complex online systems, specially for education - I've build Service Design Network (a subscription-based journal and resource) and "Faculdade Canção Nova" (the site and online services/systems of an university) from the ground up.
I've left the price a little on the low end since this is my first project here on Freelancer.com and I'd like very much to work with you.
Your project description is very detailed, so I have little to add - the application will behave as you outlined (I may have a few suggestions - eg. allowing students to login using their Facebook accounts; but we can discuss them later).
I intend to develop the application based around Wordpress, a leading plataform for content publishing. This is advantageous because it allows the "site" parts (the static content and pages that will attract and inform users) to be easily managed, and the overall design can be very modern and professional; and also easy to maintain and change.
Included in the price is the creation of the entire application - it's visible frontend for students, and the management 'backend' parts. Included also is the initial setup of the application with a hosting provider of your choice. Please note, however, that creation of design elements unrelated to the site are not included - so you'll need to provide the logo, colors, etc of the company in question.
I'll be eagerly waiting your response.