Thanks for your info.
I'm starting to play with Mason, and yes, FastCGI is certainly possible. I did consider it since I was planning to keep using shared hosting (before getting to know DreamHost plans). However, I find mod_perl relatively simple to configure at this point; I've successfully used it with my machine's server. I didn't had success with FastCGI though, which requires some knowledge to write a handler that I'm still studying.
Or maybe, within some time we'll be able to use PSGI as well. The PSGI/Plack adapters for both Apache and FastCGI are there, but I didn't managed to get them going yet. Seems to be pretty "advanced" stuff.
So, as you can see I'm still learning a lot when it comes to servers.
Regarding installation of Perl modules, I found this page with some instructions. Anyway, just to confirm it, with the root user access I should be able to install any modules on my VPS in the traditional way, and avoid extra configuration on my scripts to modify the modules search path, right?