Hello, I've read the attached document in its entirety. I can do this project for you without any CMS, but not sure that it be good idea not use any framework for this system (like CakePHP or Codeigniter). In fact most count of programmers will use own code (framework). My thing that be better if you will know what framework, and it be popular framework. It help to extend and support your project in future, so I plan use CakePHP and Bootstrap CSS framework for backend(admin part).
Also have two small questions:
1. Search, is it must search only by products or something more?
2. User Levels, is it be described at once and we will have hard coded types with access or you need full ACL system, when you can create user type, manage access for this type, create users of this type.
(From my practice, last system is universal, but very difficult to use for admin, increases development time and difficult to support in future, get additional time and money)
Thank you for you description of project, will be glad to work with it.
Regards Denis.