I'm going to assume that you are making all of your accommodation reservations well in advance of your trip. If that is the case, then your arrival/ departure dates for each city are nailed. So there is no reason not to also nail down your travel arrangements for those days as well. And since the prices are so deeply discounted for tickets bought well in advance, I see no benefit at all in paying so much more for a rail pass plus added costs for seat reservations.
Having said that, a couple of comments on the itinerary. I agree that your time might be better spent by going directly from Sorrento to Florence, and adding the Rome days to the end of the trip. Go to Siena by bus; Lucca by train. But please don't shortchange seeing Florence at the expense of these if you haven't been there before. It's a wonderful city. This is one instance where I wouldn't buy train tickets in advance. If you want to spend more time in Florence, ditch one of the day trips. As for the "etc", I don't think you have time for that, unless you mean to include Pisa on your Lucca day.
If you're only staying in Verona for 3 nights, I don't think there's enough time for any "etc". I wouldn't want to only do Venice as a day trip, since my favorite times in that city are very early mornnings and late evenings. But that's just my opinion, and your priorities are likely different.
ETA I would never recommend renting a car for a trip like this. Parking would be a nightmare, never mind trying to avoid all the ZTLs and the cost of tolls. We've done driving trips in Italy, but only when travelling in rural areas of Tuscany and Umbria where it made sense. Even on some of those days the drive consisted of going to the train station and then back to the agroturismo that night.