Traveling from Tuscany to Amalfi Coast

Can you fly open jaw, say into Florence and home from Naples or vice versa so you are not back tracking?

You'd travel by train from Rome to Florence. By bus from Florence to either Lucca or Siena. Then by train down to either Naples or Salerno and from either of these on to Positano via train/bus/ferry depending on the routing you choose. If you just Google things like "bus Florence to Lucca", etc, you should turn up all the train & bus (& ferry) links you'll need. The national rail system website, which you can see in English, is http://www.trenitalia.com/ There are different bus systems in different parts of Italy. Googling your specific route should direct you to the correct ones. Most bus system websites are in Italian, but you'll probably figure them out once you've looked at a few.

The logical order for this trip would be to fly into Pisa, train from airport to Lucca. Lucca- train to Florence- bus to Siena- train to Rome- train to Naples-circumvesuvian to Sorrento-Fly out of Naples Transportation costs for this route should be under E100
You could also do this in reverse

Thank you very much! All of the respones are very helpful