I suggest that you start by fully-specifying the site ... including detailed mockups of each (and every!) page, and all of the system’s behavior. Next, armed with this detailed plan which will take you quite a bit of time to do, systematically hold it up against each of the frameworks aforementioned.
mod_perl, vs. CGI vs. FastCGI, is a deployment decision that you don’t need to be concerned with yet.
It might seem odd, at first, to think that you are “really doing work” when you are not “writing any [Perl] code,” but so it is. Every building is built entirely on-paper first. That just might be the most-important lesson in programming that there is, and it’s one that is sometimes never learned in a long career.