Which PHP framework should I use?
DO NOT USE CAKEPHP See commandment #5.
You have a choice between Laravel and Symfony. Use the former if you're unsure.
Previously, I strongly recommended Kohana. Sadly, however, it looks like the developers have forever given up on writing anything but the most basic of documentation.
The fact that a common response to this lack of documentation is "read the source code!", along with breaking code changes between minor releases, makes it hard to continue recommending Kohana.
Once more for the hard of hearing: DO NOT USE CAKEPHP See commandment #5.