One of the great perks of PHP frameworks are that they minimize reinventing the wheel in a great number of common web application needs. Security issues, graceful exception handling, RESTful URLs, and reusability of code across your site are fairly universal considerations.
It may be easier to familiarize yourself with the tools of a framework and then see if you want to take on the full MVC system it supports. For that end, I'd suggest familiarizing yourself with the Zend Framework. ZF works as a library of classes which can be implemented individually for particular uses--anything from security to Lucene search--but contains classes which, when used together, implement a fully fleshed out MVC paradigm.