First of all, welcome to perl. Come in, make yourself to home, and hope you enjoy your stay.

As an initial recommendation, from what you mention, I would suggest Learning Perl (AKA the Llama book), Programming Perl (AKA the Camel book), then Perl Cookbook. The first of these will help you in getting used to Perl, the second gives you a deeper technical understanding of it (and serve as a good reference), and the latter gives a number of examples of solving relatively common problems in Perl. Some people will go to the second and go back to the first later, especially if they have some previous programming experience, but in general those three would be a good starting point.

In addition, you may also wish to refer to the Tutorials section of this site, as well as posting here and reading the posts of others.