Arriving in Rome, get to the Tibertina train station and buy a ticket for Florence. The machines accept a CC with a pin #. The trains are frequent and take 1.5 hours.
Tickets for Venice, Naples and back to Rome you can buy on the Trenitalia web site up to 120 days in advance.
Post a question Naples to Positano, where you use a different system, and there are options.
On www.trenitalia.com click the UK flag for English first, the use station names as appropriate - Fiumicino Aeroporto, Roma Termini (or Roma Tiburtina), Firenze S. M. .Novella, Venezia S. Lucia and Salerno.
For Rome to Florence, buy at the airport if heading straight there on arrival, in case your flight is delayed. Otherwise buy in advance to save money.
Ferry from Salerno to Positano here coopsantandrea.com/it/…
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