Should I go for Learning Perl or Beginning Perl?

Yes. :P

Jokes aside, I would actually recommend neither Learning Perl nor Beginning Perl, though I'm sure that they're both excellent books. The one that introduced me to Perl was the Camel, a.k.a. Programming Perl.

This one'll serve you well both as a textbook and a comprehensive resource for quickly looking things up later. It's not aimed at beginners who're not familiar with no prior exposure whatsoever to programming computers, but it's exhaustive, accessible, and (above all) a pleasure to read.

Even if you decide to buy one of the other two, you'll want to buy the Camel sooner or later. So why not start with that one? You might find you don't even need another one.