Under EU rules, as the spouse of an EU citizen, you are entitled to a free visa. However, since your fiancée is Italian, and you wish to enter Italy, you may be required to work under Italian law rather than EU law. I looked at the Italian governments website, however, and did not see any indication that they have different rules for Italian citizens' family members. It was a brief look, however, so I may have overlooked something.
(If there is a more restrictive regime for family of Italian citizens, you could get around this by first moving to another EU country. This is useful for people going to the UK because UK's spouse visa rules are much more restrictive than EU rules. This is known as the "Surinder Singh" route.)
Regardless, you will almost certainly need to get your marriage recognized by whatever country you're applying to. Typically, that involves getting an apostille from the country that issued the marriage license, which attests to the legitimacy of the license document. You would then present these documents as part of your visa application.
If you need to register your marriage officially with the Italian authorities, it may be that you can do it at the consulate, or perhaps you would do it after you settle in Italy. If it is a prerequisite to getting the visa, then you ought to be able to do it at the consulate. (It would not make a lot of sense to require you to travel to Italy first, in order to prove that you are married, so you can apply for a spouse visa!)
All of this assumes that you are not a citizen of one of the countries whose citizens are eligible for visa-free short visits to the Schengen area. If you are, then you would not apply for a spouse visa. Instead, you would travel without a visa, and then once you get to Italy, within 90 days, you would apply for a residence permit.