My family and I are in the midst of a two-month Italy stay right now. My husband and I are remote workers in our mid-thirties, with a 5 year old son. We rented an apartment for one month in Treviso, and are in Mantova/Mantua for the month of July. We had been planning this trip for about a year.
No official documents needed, except passports. We have COVID vaccine cards but no one has looked at them. For us, because I was traveling by myself with our son, I did travel with his birth certificate and a notarized letter signed by my husband that I had permission to take our son out of the country by myself. But no one needed those either, thankfully, and I don't think that applies to your situation :)
The hardest part for us was determining where, specifically, to use as our bases. I speak some Italian (I was more or less fluent in college 15 years ago, but have sadly lost most of it), so I wanted a city where I could immerse myself in the language (off the radar of the typical American tourist). Not too big, but not too small. In the northern part of the country because we haven't explored these regions as much. Historic, walkable core. Parks for my kiddo. Good wine region. Easy to travel to other small towns. Safe, where I won't have to be watching my wallet at every turn.
To help narrow down the cities, I actually made an excel spreadsheet. I kept a list of potential cities and then marked off whether they had the characteristics we were looking for. I knew we would want to rent an apartment, so I also checked Airbnb for locations to make sure there were suitable places (at least two bedrooms, fast wifi, AC, walking distance to stores) for our dates and in our price range. Also, I used Google Maps street view to help get a feel for the neighborhoods/cities.
Then I checked out every Italy guidebook from our local library. Rick's books are great, but they have a lot of information on fewer places, whereas other books provide a little information on a lot of places. In the end, the cities we stayed in, and most of the cities we visited, aren't even mentioned in Rick's book.
It was a LOT of planning. Fortunately, like you, I truly enjoy it. And this opportunity, to live in Italy for two months, has been absolutely incredible. There have absolutely been hard days. I've made countless language blunders. My son had a stomach bug and I had to carry all forty pounds of him for fifteen minutes across town to the only pharmacy that was open on a Sunday. Things are simply not as convenient as they are in America. Living in a country (even for a few months) is vastly different from being on vacation. But overall, it's been magical. My family and I are already planning to do it again next year, whether in Italy or another country in Europe, we're not sure. Please keep us updated on your trip planning progress, and I hope you'll give us an update on where you choose!