I too assumed that it would be both cheaper and faster (non-stop) to fly from San Francisco to Rome than from SFO to Florence. Surprisingly, in all the time I've researched airfares I've never found that to be true!
I've found travel time is the same (one-stop;16 to 19+ hours. I will pay a bit more for the 16 hour itinerary) and the price is the same as well.
So, unless you're really getting a deal, fly in/out of Florence. The small airport is very nice, low- stress. You have to take a bus or cab to the train station.
Depending on which airline you like, prices to Milan are comparable to Florence, but that doesn't seem too important here, unless you want to fly open jaws. To that end, I've found United/Luftansa flights are competitively prices for open-jaw itineraries for Milan & Florence. Contintental has sales right now and has good prices to Milan--but not Florence so that won't work for you.
FWIW Delta flies from SFO to Pisa with one stop in the US--I believe that stop is either JFK or Newark. But, I'm getting far afield of your request.