My last two trips to Italy (2021 and 2022) were both in September/October, so it’s a good time to go. Generally (except for Cinque Terre) it wasn’t excessively crowded, and aside from a few rainy days, the weather was pleasant.
I hope, though, that your planned itinerary isn’t completely in the order of your list. Crossing Italy from Venice all the way west to the Cinque Terre, then rebounding pretty far east to Bologna is a lot of back and forth. Regardless of the sequence, it’s ambitious, but at least you’re not planning any one-night-stands, and some destinations are for three and even four nights, so it’s not completely unreasonable. Still, if you kept all these, go from Venice to Bologna, then to Siena, then Florence, THEN Cinque Terre.
Actually, here’s my two and a half cents worth: Cinque Terre, even in late September/early October, was waaaaaay too crowded, and unfortunately, not a place I’ll recommend any more - or a place I plan to return. We first went there in June 2001, and it was magical. Returning in October 2021, we were among the hoards that had descended on the towns and the trails. We’d made restaurant reservations at a couple of places in Riomaggiore, and they were OK. For other nights, we couldn’t get into some places - they were booked. Other places weren’t open - apparently closed for the season, or open on very limited days or hours. People pushing, yelling, cutting past. Shoulder to shoulder mob in Vernazza. this wasn’t supposed to be like the Subway at rush hour - not enjoyable. And we had a rental car at the time, and drove straight from the Cinque Terre to Bologna to turn in the car - long distance, as I said earlier, not the most wonderful situation, with lots of road construction delays. Maybe a train would be easier, but it’s still long, so avoid directly connecting Cinque Terre and Bologna if possible.
Really, skip the Cinque Terre and add time to Sorrento. Stay there, and also visit Naples as a daytrip(s) from Sorrento. Is Pompeii/Herculaneum/National Archaeological Museum/authentic pizza part of your Naples plan? The Circumvesuviana train links Sorrento and Naples.
Italy has 2 main train companies - Trenitalia (owned by the government) and Italy (private company). Italo goes fewer places, and may or may not be cheaper. Many of their trains tend to be faster, but again, don’t go everywhere. Trenitalia has some billet trains on some route, and slower trains on others. Each has its own Website, and you can reserve tickets there or at a train station, but I’ve found the Trainline app to be extremely convenient for trips throughout Italy. Download it and try putting in some locations to see how it works.
IF you cut out some destinations and needed to cover more ground (say, Venice to Rome), flying could be an effective way to get from Point A to Point B. You’d have to weigh the flight price and the time to check in, go thru security, collect bags if you check them, etc. against the time and expense of other means of transportation.
Enjoy your trip, however you do it. Rick Steves’ advice is to assume you will return, so you could split Italy into north and south, and see one part this trip, and the other on a future trip, if you decided you didn’t have to see it all this one time.