Okay, if you're learning Perl to become better at programming in general, then that's probably not the best choice. Perl is an unusually powerful and dynamic language, and there aren't that many languages that share its quirks. I recommend C as a "starter language" nowadays. :)
However, if you're learning Perl for those reasons, then I'd recommend "The Llama Book" (also known as Learning Perl). You may also get "The Camel Book" (Programming Perl), though you may have a much harder time learning Perl with that book and I'd recommend saving it until you're a bit more experienced. ;)
I uses Perl for it's regular expression, pattern matching, file operation exclusively. It is not exactly a neat language in terms of syntax but it excels in certain areas which I like.
But one warning to note. When you delve deeper into Perl and come to it's Object Oriented Perl, I guess OOP purist will *shout* at it's implementation :P
However I do marvel at Larry skill in adding Object Oriented feature to a procedural language. Maybe a classic learning lesson for developers who want to add OO to a procedural language and yet not having to tear apart the existing procedural language core syntax and engine :P
Well Perl library developers are taking all those in their strides. Look at their code, they uses them so extensively that it is a testament of how "twisted OO" still has their fair share of developers :P