Hi and welcome!
JFK does have the most options for getting to Italy - AZ, DL & AA to MXP & FCO as well as EK to MXP. Unfortunately, the terminals are not connected so you will need to decide which airline you are going to take. Not sure if we have anyone from AZ or EK (Mig?) but there are plenty of helpful folks here who could help you out with load info on AA & DL. For AA, the FCO flight ends at the end of Oct (last flight to FCO on 10/28) but the MXP flight runs for the whole month. When I went about 9 years ago also in October, AA didn't fly to MXP yet. We flew into Rome, went south then back north ending up in Milan. We then took the train from Milan to Zurich for the ride back across the pond. ZED tickets are good for 90 days from when you buy them but you should be fine purchasing and listing about a week before you travel. Buy one ways to make refunds easier. If you have any further questions, feel free to ask.

I would highly recommend the Rick Steves Italy book. It was spot on for finding nice, affordable places to stay and eat. Found a gem of a place in Florence but of course, I didn't write the name of it.