I would suggest you to create the site structure in BEdita using
"publications" module for sections (which is a container/collection of
contents and it is usually used for organize them and to create menus in
frontend applications) then add "documents" and "multimedia" contents to
this sections.
For your frontend application I would suggest you to start with the
example frontends in BEdita package: html5.example.com for an HTML5
"dummy" frontend to use as a basis for new frontends, or wp.example.com
to have a look at a working example.
Access to sections, subsections and contents via urls is already handled
by BEdita, you don't have to care about that.
You may easily add your application logic to
controllers/pages_controller.php
Hope it helps.... if you need other suggestions or have other doubts,
please ask!
ciao
Stefano
Suggestion :
a tiny tutorial on how-to migrate from a cake php site with multiple controllers to a BEdita frontend.