I believe both pricing structures have lower prices when they release fares and they go up as the allocated tickets get bought, so earlier you buy them the better. The multiple locations on the Italo website that I checked didn't note any particular method of age identification, but since you will have your passports with you, that's as official as you can get. The conductor may ask to see them if absolutely necessary, which I doubt (there aren't any other places I could see them being able to check, unless you have to pick up your tickets at a counter). I would agree with the previous poster for the likelihood of getting a newer train, and I had forgotten about the wifi!

I went in 2015 to Italy and I did all trenitalia except from Salerno-Venice because we didn't have to change trains, as I felt comfortable booking either one, but more or less went with the one that the schedule/price worked best for us. My last trip in 2019, none of the Italo destinations or timetables worked for us.