Use either OS, depending on your preference. If you're equally comfortable with Linux and Windows, then I'd suggest Linux -- but there's no reason you shouldn't use Windows to program Perl, if that's what you like.
Typically, Linux distributions come with the Perl interpreter already installed. Invoking Perl scripts from the command line is easy: Just include the hash-bang path to the Perl directory at the top of the text file before including modules -- something like this:
#! /usr/bin/perl -w
use strict;
... and then use chmod to make the file executable.
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You can also script Perl in MS Windows, but first you'll have to spend a bit of time setting things up. You'll need to install a Perl interpreter such as Strawberry Perl or Active Perl. This may involve changing some system settings, but once it's all up and running, it will work pretty much the same as it does in Linux.
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Whichever OS you decide upon, I recommend you get your hands on the wonderful book "Learning Perl" from O'Reilly Media. It's highly readable, written in a conversational and even humorous tone, and it comes with lots of easy-to-understand examples. (I'm not associated with O'Reilly, but I speak from experience -- after wrestling with the Perl FAQ and other dry, complicated resources, I found this book to be the most straightforward introduction to the Perl language.)
There are also lots of learning resources available on the Perl.org site.
Perl is a great and witty language for getting things done. It's well worth the effort. I hope you enjoy learning it!