I may be a little biased because i earn my money from making stuff with Perl. When i say "doing stuff with Perl", i don't mean scripting. I'm talking about big projects (new and old) that are production critical.

One the the reasons we have chosen Perl is its huge library of existing code and also the general strive for backwards compatibility. In business, that counts a lot more than being hip/cool/whateveryoucallit. Basically the same reason, why there's a lot of Cobol, Fortran and Lisp code still in production all around the world.

Actually, choosing a brand new language as a career path is highly risky. Only a few companies try it out and there's no notion of job security because there's not much of a codebase to maintain. Python is far past that stage, but to be honest, i haven't yet encountered many big projects in my business that actually use it.

When it comes to "Big Data", your number one priority is certainly to learn your way around databases. Depending on what interests you, you might find it useful to learn some NoSQL stuff. But there's no way around learning at least one of the "big" SQL databases (PostgreSQL, Oracle, Microsoft), because there are a lot of business cases where using a fully ACID compliant database with features like Foreign Keys is absolutely essential.

Now to the question if you should learn Perl: Yes, you should. Perl is (in my opinion) probably the language best suited to process text-based data and also has a lot of libraries to handle scientific computation. And if you think about it, a lot of data you'll encounter in your work life will be text. HTML is text, accounting and warehouse managment is text-based (plus a few big red numbers), reading some spreadsheets into a database (or generating spreadsheets from databases) is also mostly text processing.

Which version of Perl? Well, i would say go for Perl 5. This is currently the Perl version used in businesses, since Perl 6 is new, completly different and still has a relatively small amount of existing libraries to use.

Now, that said, will Perl and (say) PostgreSQL be enough? No, you should also learn at least the basics of HTML and Javascript and even (ohmygodimsayingthis) PHP, everything seems to drift towards "web-based" and "cloud" at the moment. Even if you don't do web programming for a living, you might be able to fatten up your piggy bank with a little (tax free) support for your relatives This-is-my-dog homepage. Just saying... (Working for relatives often will make you feel dirty but not rich, but when you're broke you're broke.)

Also taking a few weeks learning the basics of C will be a good idea. It's low level and rather primitive (from a Perl developers point of view), but it's perfect in itself. It's also dead useful for nearly everyone using a high level language, because sooner or later you'll want to use and understand a few of the millions of pre-existing C libraries or even implement your own for speed or do something (censored) to a poor little device.

Of course, these are only my undef cents