How far back does your claim to Italian citizenship go? I'd imagine you at least need the birth certificates (or maybe just passports) of the ancestor(s) who came from Italy, and their marriage certificates and birth certificates of those who are descended from them to include you. Might be a PITA to chase down but worth it.
BTW, the previous Berlusconi government also set aside a number of seats in the Italian legislature for overseas Italians to elect representatives to (yes, Italians who have never been to Italy can vote in Italian elections).
I don't know your age, but I would check carefully to make sure you're exempt from any unpleasant side requirements of Italian citizenship before signing up.
That's true of a few other countries. Austria for one though it seems Austrian males not residing in Austria for any length of time are largely exempt, and can elect to do slightly-longer community service in lieu of military service.