Hello medgin, and welcome to the forum!
The first thing you need to lockdown is the amount of time. With 10 days I would recommend three places at most and organized in a way that minimizes travel time. With 14 days you can start to expand your options some but this list of places you have is literally from one end of Italy to the other and is too much for even 14 days because of the distance and Sicily will require a flight to and from which adds a lot of time and hassle. Also be aware that the Amalfi coast involves complicated travel logistics as well so you need to allow more time to get to and from there. If you visit it as day trips from Salerno it will prevent some of these delays.
When is comes to planning the most recommended way to this from these boards is to count the number of nights you're staying and not the number of days. This aids in planning where you will sleeping every night, rather than where you will be during that day, which helps with hotel planning as well. Keep in mind that 2 nights in a place allows only one full day there and then two partial days where you'll need to worry about baggage and transportation. Do not underestimate how much time it takes to get everyone packed, checked out of the hotel and then to check in and unpack on the other end. Limiting the number of times you transfer accommodations will cut down on this process. I would never recommend staying anywhere for only 1 night unless it is purely for travel logistics - like being in the city you are flying out of the night before. I also recommend allowing an extra day after landing to allow for jet lag, acclimation and travel logistics because you may not be up to a full day of packed itinerary just off the plane.
So I would recommend making a list of each night, where you're planning on staying and any time travelling between these locations on the day you will be transferring from one place to another. I personally use a spreadsheet but a simple list works just as well. After you have a number of nights laid out I would count the number of days (nights -1) and list what you want to see and do in that place and see whether you have enough time. Then look into travel time between locations and plan for those travel days.
A site like Rome2Rio.com is a good place to start investigating potential travel times and options as estimates. But always confirm what they are telling you on the actual modes, dates and times you are traveling. For instance there is no train access to San Gimignano so it takes a combination of train and bus or some other means to get there.
Time of year has a great deal to do with planning and crowds - especially places like the Amalfi coast that has definite seasons and much is shut down during the off season.
Look into "open jaw" or "multi-city" flights like flying into Venice and out of Rome to save time re-tracing your steps to get back to the city you flew into.
A great place for train information is the Man in Seat 61: https://www.seat61.com/train-travel-in-italy.htm
As previously recommended RS has a huge trove of how-to and what-if information for travellers. Many of us here have benefitted from Rick's lessons, books, videos and other information and return here to get and give advice. I highly recommend starting with a book or two and some of his videos and articles to refine your plans and pick up great general travel advice.
Good luck with your planning and come back for advice on your itinerary and questions about destinations,
=Tod