Well, without any specifics of your task you are basically asking for statistics on CPAN module usage. :)
I'd say that, considering the fact that most Perl programs deal with web and databases (at least throughout my experience), you will not waste your time if you'll brush through
CGI and
DBI. But that you already knew most probably. :) So, you might try something that works with dates, like
Date::Calc or
Date::Manip. Maybe, some database abstraction modules might do some good - check out
Class::DBI and
DBIx::Abstract.
That is as far as I can go without specifics. :)