10 nights is not enough to do the big three -- Rome, Florence and Venice -- as well as Buccino. Is Buccino set to be your last stop? Assuming so I suggest that on arrival in Naples you proceed immediately to Rome by high-speed train (only takes about an hour). Spend 4 nights in Rome, then go to Florence (again, high-speed train, about 90 minutes) and stay 3 nights. Finally a high-speed train to Salerno from Florence, for your final 3 nights in Buccino. Perhaps while you are there you can get to the Amalfi Coast. You'd need 2-3 more nights (total 13 would be nice) to make going to Venice worthwhile. If you have that 11th night, add it to Florence and spend a day going to Siena.
Have you read a good guide book yet? Like Rick Steves' Guide to Italy? Essential to planning and implementing. Everything you need to know about trains is explained in the book.
It is getting very late to be making reservations for high season. You will need to secure your lodging ASAP.