I know that a lot of people swear by the O'Reilly books, and I like them too, but I also really liked "Elements of Programming with Perl". It's really easy to read, and there are exercises for each chapter.
It's a really good book. It teaches programming using
Perl as its language of choice. The drawback is that once
you get through it, it's not much of a reference. It is most certainly
geared for the beginner programmer, although, I have to admit, it has
some nuggets in there for an old miner, too. I think of all
the books I've bought on Perl (And I think I should own a bit of O'reilly)
So far the book I've enjoyed the most has been Object Oriented Perl. It's
not really a beginner's book though. The Programming Perl Book is more of
a reference manual than a tutorial. For an introduction to the language,
Elements of Programming is probably the best of the beginners books I've looked at.
(I won't look at the dummies books. I find their titles insulting... absolutely a
marketing ploy).