I suggest taking the Bernina Express train from Switzerland into Italy and make an overnight stop in Varena to enjoy some walking along Lake Como and maybe take a ferry boat to Belagio for a short visit. After Varenna, take the train to Florence for 3 days. You can easily spend all 3 days here, but I would consider a day trip to Siena as well. Finish your trip Rome. An alternative would be to visit the Cinque Terre after immediately Switzerland. Getting there really depends on where you will be in Switzerland but you could potentially fly into Pisa or Genoa and take the train the rest of the way, or you could just take the train. I would spend 2-3 days here visiting the towns and hiking. From there take the train to Pisa for a few hour stop over to see the Leaning Tower and then head into Rome ( this will take up one day). Spend the the last 3 days in Rome.
Once you have Switzerland figured out, you can better plan Italy. For flights, check skyscanner.com and check seat61.com to get the best information on train travel.