Others have written that OO and modular programming are somewhat orthogonal. So, if modules will enable you to refactor and reuse your code as subroutines, that is the simplest path forward. OTOH, if you are using complex data structures, or families of data structures, OO does help by keeping the code for initializing these structures and methods for operating on them in one place.

If you haven't experienced how OO can help you organize your code, it is definitely worth learning, IMO. In that case, I find vanilla perl OO to be a good starting point, since you can see how it works more easily than with an OO framework. I started that way, then began using Object::Tiny to create accessors. In a new project, I would probably try Moo and friends.