Hello forbess1234,
The Railpass is a somewhat antiquated model at this point and I wouldn't bother with it.
Nothing you have listed here suggests you would need a car.
Most of the legs you mention are big, intercity routes that are served by fast trains - either Frecciarossa run by Trenitalia or Italo Trains run by a private company. Fast trains come with assigned seats, levels of amenities and should be booked as early as possible for the best pricing and to reserve your seats.
https://www.trenitalia.com/en.html
https://www.italotreno.it/en
Aside from choices of amenities the classes of fast train tickets are dictated by their flexibility. Consider this carefully - especially following a flight or something else you can't control. If you book a flexible ticket and miss or want to change your train you'll have to rebook it with an agent. If you buy inflexible tickets and miss your train you're out the price of the ticket.
Smaller Regionale local trains or trains like the Circumvesuviana that runs from Naples to Sorrento do not need to be purchased ahead of time and can be purchased at the station and for Trenitalia trains on-line or from the app. I recommend getting and using the Trenitalia app for dealing with trains.
Large intercity trains tend to be reliable and generally on-time and immune even to short term strike actions. Regionale trains may require a little more slack in your schedule. But realistically you may occasionally brush up against the controlled chaos that makes Italy so appealing to those of us who love it when dealing with trains and schedules in Italy.
Good train advice for all over Europe is available here: https://www.seat61.com/
Without seeing how many days you're actually spending in Italy I can't say whether I think your schedule is overloaded but you list a lot of travel between big places. If you lay out how many nights you are staying in each place and what your interests are it would be clearer as to whether you're spending enough time in each place or trying to do too much.
My generic advice is layout the nights you're spending in each - where you are sleeping - and how much time you're spending on travel between places on travel days. Keep in mind 2 nights somewhere is 1 full day not 2 days. And that changing cities means packing, checking out, travelling with bags, and finding the new place and checking in there. That process with the required travel time added can keep most or all of a day. I would never stay somewhere just one night unless travel needs - staying the night before a flight - dictated it.
Just be sure you're not spending too many days or your vacation on intercity travel logistics. My general advice on Italy is slow down enough to be sure you're able to appreciate the Italian la dolce vita that is a real part of the Italian experience and not rush through and miss that part of the experience.
Have a great trip,
=Tod
