As suggested by many others here, I would recommend "Programming Perl" (By Larry Wall, Tom Christiansen, Jon Orwant), which is perfectly suited for a beginner in the language as well as in programming in general. It nonetheless gives a very good insight into the language and might be a good "companion" for quite some time.
Now, concerning your second question... Well, if you have the choice, don't go for Perl, it is kind of messy and seems to be superseded in many ways by other languages. I don't know Ruby, which is often cited as a good alternative solution, but I can clearly recommend Python. Better syntax, object oriented... All my friends who made the Journey from Perl to Python were convinced within a week.
I'm not sure about a good book. I've been learning it "as I go" while learning advance techniques in Linux, but generally the most useful thing about Perl is learning it's pregex or Perl Regular Expressions and of course to make fast scripts to automate processes in unix-like operating systems, such as program installation, in-development processes that are repeated regularly etc.
A very good (and funny) introduction on Perl language is in "Minimal Perl: For UNIX and Linux People" by Tim Maher which describes step by step the basics of this language, from one-liners to scripts. I think it is a better introductory book on Perl than "Programming Perl" or "Perl Cookbook" while both are excellent by the way.