I'll second Acrochik's suggestion for Lonely Planet. I've used them for everywhere I have travelled in the last 10 years and they are far and away the best guide for the kind of travelling you want to do.
The wife and I spent three and a half weeks touring Italy in 1998. We travelled by bus and train. Italy is set up perfectly for that kind of travelling. The only thing you can't do is visit some of the out of the way spots in Tuscany, but for hitting the highlights it is the way to go.
I'll also second that 3 days in Rome is the bare minimum if you want to get more than a passing glance at everything. We did 4 with a day trip to Hadrian's Villa on one of the days. Be sure to read the Lonely Planet guide carefully as to when certain musuems/venues are open and plan accordingly. Sometimes you can get caught out if you haven't researched well and the place you want to see is closed on that particular day.
Our plan of attack for touring is to stay near train stations. In Italy, there are always numerous hotels/pensioni near the train station. The added bonus is that in Italy they are also very centrally located. In Venice, for instance, you have to be careful when exiting the train station or you'll walk right into the Grand Canal. This while the airport is over 20 miles from town.
I almost never make reservations. If I do it is because I know the place or suspect it may be busy when we arrive. Always plan to arrive at a new place by noon. That way you can find a room with ease before they get booked up later in the day. I'll usually have a list of places from the Lonely Planet guide to go check out. I'll leave the wife at the train station with the backpacks and head out for a recon of the hotels. This way I can make sure the room offered is going to be clean, quiet, and comfortable. We averaged about $45.00 per night during our trip, but that was before Italy was EUROfied. It would be at least double that now. Rome was the most expensive. I did get my parents a place in a 3 star hotel near Termini last year for 80 Euros. It was January so the rates were lower than normal. The room was very small and basic, but that is how it is in Europe.
Florence can be a good base, but you can easily see the whole city in two days. If you do run out of things to do while in Florence then take a half day trip to see Pisa. It is a short easy train ride to Pisa and the busses outside the station go right to the leaning Tower. Sienna is another town well worth seeing and the aforementioned San Gimignano. Sienna is easier to get to and has more accomodation.
For Capri you really have two choices. You can make it a day trip from Sorrento or you can spend the night or a couple of nights. The advantage of staying the night is that the tourist hordes usually make it a day trip, as the price to stay overnight is quite high. That leaves you and a just a few others to enjoy the island at night ( unless it is Friday or Saturday night, then all the revellers are out for the weekend ). We did the day trip option, but it really isn't enough time to properly see the whole island. I would go for two nights mid-week, as that would be optimum. I would also try to get a private room in a villa or house as oppossed to a pensioni.
The Amalfi Coast is quite spectacular as well and a day or two in Sorrento exploring the coast and perhaps up to Pompeii would be worth the time. No real reason to go to the top of Mt. Vesuvius unless you really like climbing dirty mountains. While we are on the subject of the south, I would give Naples a clean miss. Read Lonely Planet and you'll see why.
Just one other thing, for the type of travelling you want to do make sure you both have money belts. Petty crime and pick pocketing are something you need to be aware of. I like the Eagle Creek money belt that I keep strapped around my waist with passport/credit cards/cash in it. It is always underneath a shirt so there is no way it can be stolen, short of someone undressing me in public

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Hope that helps,
TP