Miami to Rome on a 777-220 and stressed about turbulence and more

I have to connect in Miami for a flight to Rome in a few weeks and I realized we will be there in the middle of hurricane season. I am terrified of over water fligths and turbulence and the 777 is, to me, an ancient plane. What are the chances our trip will be messed up by weather, and if if does take off, how bad is the turbulence on that route? IF any of you have flown a similar route this time of year let me know!