There is nothing other than 1st or 2nd class. In general I would not be flashing around too much cash or jewelry, like you wouldn't in New York or London.
I woud advice to plan in advance so you can book first class on Italo trains (one of the two companies) which are cheaper than Frecciarossa if booked in advance - and first class is quite cheap, compared to UK.
And book Hotels in all town which would allow you to walk in the center of Florence, Rome or Venice.
Can give you more advice about food and things in Florence which is (was) my hometown.