I hope you have been encouraged by the replies you have received so far. I can't add much to the many excellent suggestions made but one book that I enjoyed and found very useful was Effective Perl Programming by Joseph N. Hall and Randal L. Schwartz. It covers the fundamental topics effectively by breaking things down into manageable chunks with clear explanations.

Keep plugging away and gradually all of the seemingly disconnected bits of Perl knowledge will start to mesh together and, before you realise it, you will be thinking Perl.

Cheers,

JohnGG