Welcome to the RS forums, Daniel. :O)
You've already been given excellent advice above that I'll just echo: go to the bookstore and library and get your hands on travel guides about Italy and, more specifically, the 3 cities you are planning to visit. As you browse, jot down attractions and activities which will appeal to you and your group, and then come back with any specific questions about them you may have. Oh, and assuming your travel companions are old enough to pack their own suitcases, get that group of yours to help!
See, not knowing anything about you or your group, we've no idea what to recommend. I can, for instance, send you to churches and art museums all day long but if you don't care for those, then I haven't been any help. Accommodations? How much do you want to spend per night and how may rooms will you need? Do you normally prefer budget properties or posh, 5-star hotels? Lots and lots of variables....
Additionally, the forum history is a wealth of info so you can search, say, for recent discussions/articles about accommodations or restaurants in Florence, Rome or Venice, along with other topics. See the search box at the very top of this page? If you type "restaurants, Rome" into the box and hit "go", it'll take you to a list of prior discussions/articles.
If you then click "travel forum" in the grey box on the left: that will narrow the search JUST to forum discussions. Then in same box, you can narrow further to most recent threads under "filter by date" to only those in the past 2 years, 1 year or 6 months.
12 days isn't really an "extended period" for Italy. To realistically weigh the amount of sightseeing time you actually have to work with, it's best to count by number of nights you'll have on the ground in Italy. In other words, days spent getting there and coming home don't count. Days you transfer from one city to another are counted as partials versus FULL days, as does arrival day as it can be a jet-lagged haze and your biggest risk of a schedule delay where flights are concerned.
A terrific website for understanding train travel in Italy; spend some time with it and come back with questions? It's really not at all as complicated as you might be thinking. Seriously, if my transport-challenged brain figured most of it out, ANYONE can!
https://www.seat61.com/Italy-trains.htm
Editing to add....
One caveat about guide books? It's usually impossible for them to be absolutely current when it comes to hours, entry fees, closures for restorations/repairs, etc. so it's always best to use the websites for the attractions themselves for gathering those details. We can send you to some of those once you've sketched out a rough must-see list.