Pick any of major PHP frameworks ZendFramework, Symfony, Silex, Slim ... and build your CMS on those. Those framework already have most of components you need. Plus they have big communities behind, so you will not have to maintain that code.
If you still want to write your own framework. Take a look in to http://en.wikipedia.org/wiki/Model%E2%80%93view%E2%80%93controller for Handling requests. No need to create DB classes as PDO http://php.net/manual/en/book.pdo.php is a nice built in abstraction layer you can use.