Our very first trip to Europe was a Greece and Italy itinerary. We fell in love with Italy, not so much with Greece. We are very wimpy from the Northwest so we went in October and even then in tended to be a bit warm sometimes. But, we generally had great weather. A friend visited her son in Italy in the month of July and said it was horrid! It may not bother you as you are from Texas.
So, I would suggest April, May, October.
As @gottagocit stated, if you are beginning in Rome, the port is actually Civitavecchia. We flew into the airport in Rome and took a transfer to our Rome hotel and spent 3 nights there which barely scratched the surface. We had a blast and walked everywhere due to the location of out hotel.
We booked a shared transfer to the port and the same back to the airport from the port.
Sorry, I have no experience with MSC.