What type of testing do you intend to do - unit, functional, acceptance?
PHPSpec can be used for unit testing only but it's very, very good at it (my absolute favourite by far). It's primary a design tool - it restricts lot of things that are considered bad, for example, static methods, partial mocks etc. It's a lot less verbose than PHPUnit so it's a big bonus if you're going for readability of your tests.
PHPUnit and Codeception can be used to cover every type of testing although Codeception is less verbose and comes with built-in modules for various tasks to save time (API testing, support for multiple frameworks, database interactions etc.). It also uses PHPUnit as a dependency.
Behat is for acceptance testing but it's better suited to verify business requirements of the application. It also doesn't use PHP for writing the test scenarious. If your application has a rich domain layer, it is a really good choice for higher level tests.
I can't really say much about the integrated testing tool that Laravel uses since I haven't used it. In theory it should cover all of the same areas as Codeception so it should be a matter of preference.
If you're looking to cover the most ground with your tests, I'd probably suggest PHPSpec and Codeception or Behat.