Frameworks like Mojolicious, Jifty (http://jifty.org/) and Dancer (http://perldancer.org) are much quicker to get up to speed on, but suffer slightly from having a smaller community of users and developers.
I've been playing with non-Catalyst frameworks a bit recently as I've been pondering a little bit of product development on an in-house project.
Of the non-Catalyst Perl web frameworks Dancer is my favourite http://perldancer.org/. For my money it's a neater package than Mojolicious, which takes the no-dependency thing a little bit too far for me. Dancer's non-OO DSL declarative style seems to work quite well (it's very heavily inspired by Ruby's Sinatra).
I'm going to give Dancer / Plack a whirl as the basis for a non-trivial app soon. I think it'll work quite well from my experiences so far.
(BTW - if you've not started playing with Plack in Perl - do so. Veeeeery nice.)
As to what you should learn - who knows :-) If it were me I'd spend at least a few hours playing with Dancer/Mojolicious/Jifty first - since any of them will have you up and running with a demo in a few minutes. Catalyst will take more work.