Visa/Permit for Non-EU Spouse of EU national (Milan)

Hi everyone! I am in a lot of need for some practical advice...

I am a US citizen currently living in the US, and my husband is Macedonian/Bulgarian living in Italy. He has EEA/EU rights and currently resides in Milan as a student. We are marrying in one month and I want to join him in Milan after marriage.

So he relies on family for financial support at the moment, but I have sufficient funds according to support us for probably a full year, although I hope to soon work and so does he.

I want to know if I need to apply for a visa in the states in order to go join him in Italy, or if I can fly to Italy as a 'tourist' and then apply for residence after I arrive? I heard that non-eu family members can apply within 3 months of arrival, on a tourist visa (possibly). Thanks for your help, I am really scratching my head over this. Cheers.