"I am comfortable with Spanish, but none of us has Italian. We will purchase Italian travel phrasebooks, but we have over three months to prepare for the trip. Should we invest time in conversation classes, books, videos, etc?"
The more Italian you can speak and understand, the more you will get out of the trip. Of course, plenty of people travel to Italy without a word of the language; they do fine and have a great time. But if you do have time and interest in studying Italian, it will definitely be repaid. On the one hand, you will find your Spanish knowledge makes learning Italian easy; on the other hand, you will find that you will interpose the languages (using a Spanish word instead of an Italian one, using Spanish grammar instead of Italian grammar, etc).
I'd start by getting a basic Italian course on CD out of the library (either "Italian for travelers" or the starter Pimsleur course, or something similar). Depending on how that goes, you can then decide on how far you want to proceed.
"I haven't made any plans for getting to and from Italy yet . I'll bet you all have recommendations on the subject of San Francisco to Venice and back from Rome. Of course, we will fly..."
Roberto now lives in the San Francisco area and is from Florence and goes back to Italy often, so he's the expert on that subject. While waiting for him to respond, you can start looking at Kayak https://www.kayak.com/flights?mc=y or Google Flights https://www.google.com/flights/#search;iti=SFO__2016-07-07;tt=m. Pick some test dates, use SFO to VCE for your first segment and FCO to SFO as your second segment, and see what you get.
Roberto will say (and I agree) that you want to change in Europe rather than the East Coast of the US if at all possible. You save total flight time, and it's also easier if your first plane is late. If you miss your Paris to Venice flight, there will be others that day; if you miss your JFK to Venice flight, you have to wait a whole day (if there is even space on the next day's flight). You want to be all on one ticket, so you're "protected" if there's a problem (they will put you on the next available flight).