If one can learn only 1 language due to time and job constraints, would Perl be the right choice?

Yes. Perl is the Swiss Army Chainsaw because it does everything and does it all well. No other single language IME can compete on those terms. There's no point repeating all the good reasons to use Perl here but given your restriction to learn just one language, Perl has to be the obvious choice.

If you can find time for a second language then that can be domain-driven and is probably going to be one of: C, Javascript, SQL, Go or (Larry help you) Java.