So you've taken the CT off the plate for the Amalfi instead?
Before diving in, I'll ask again what time of year you intend to take this trip?
Saturnia Hot Springs: have you researched how to get to this one? At a quick glance, it would be a real pain without a rental car, and it's not really close to anything else on your list. Just sayin' as I didn't have the feeling you intended to rent a vehicle at any point?
Rome: you mentioned in your other post that art (and food) were the goals on this trip? You really should add Galleria Borghese to your must-see list: IMHO, it's the best art museum in the city. There's a lot more to see in Florence as well.
For this trip you should fly into Venice and out of Rome.
Your order should be Venice>Florence (Tuscany day trip from there) > Amalfi Coast >Rome. If you intend to sightsee the Amalfi Coast, you should stay there. What, no Pompeii? Sure, you don't HAVE to do it but it's interesting that you've left it out as it's a very, very popular attraction for people staying in the Naples, Sorrentine/Amalfi Coasts region.
If you have 12 nights, this is what I'd do:
Venice: 2 nights/1.5 days
Florence: 4 nights/3.5 days (one-day wine tour out of the city; I've not included Saturnia) The art, the art, the art....
Amalfi Coast: 3 nights/2.5 days
Rome: 3 nights/2.5 days. I sure would like to add another one to this for some more explorations time,. As your Colosseum ticket includes the Palatine and Forum, I'd recommend doing those. You should also see the Pantheon.
You might want to consider staying elsewhere on the coast than Salerno if Capri is on your list? It's a 2-hour haul by high-speed ferry to the island from there, and same going back. Right now, the first ferry leaves Salerno at 7:30 AM, and the last leaves Capri for Salerno at 5:15 PM. This route is also seasonal, meaning the boats don't run it in the winter months (Nov. through March), which is one of the reasons I'm asking when you're thinking of taking the trip.
Budget? I'm no good at figuring budgets for other folks but I'm sure someone else might be able to throw some figures at it. Rates tend to be lower during the winter months.