Well, you need to have a copy of Programming Perl, because it's Larry's book and the major reference for the language.
I would stick with the order of the tutorial books and get Mastering Perl.
One other book I'd like to suggest: Damien Conway's "Object Oriented Perl." Very thorough, a little dated now, but the content is still valuable. You might find a used copy cheap, get the 1999/2000 edition.
Conway also did a book for O'Reilly called Perl Best Practices. Great book on programming style and other helpful stuff for Perl.