I started learning Perl in February, and after some web browsing chose to buy almost those exact books.I actually used the Win32 version of Learning Perl (Gecko) instead of the Llama. And I got the Perl CD Bookshelf instead of just Nutshell

Learning Perl (for Win32) is amazing, by far one of the best tutorial books I've read. Definitely a must read.

The others have been useful, and I recommend them. I also suggest that you consider getting the CD-ROM version of Nutshell.

In order of usefulness:

1. Learning Perl: I used this a bunch at first and occasionally for reference.
2. Perl In A Nutshell (and CD-ROM): I use this almost every day that I write code.
3. Perl Cookbook: A great sourcebook, can be a huge timesaver
4. Programming Perl: I use this one to puzzle out arcana that aren't discoverable by other means.

Good luck finding the time!