Just remember that you must be at the airport 3 hrs before international flights and some airports will not let you on an international flight if you have not checked in 75 minutes or more before the flight.
I had researched taking this same tour and many of my options were out of Atlanta and they go directly to Venice (your first city of this tour). So there are a variety of choices that allow you to sleep on the flight directly to Venice.
In booking the return flight, your options may be more difficult since you'll want to pay close attention to their arrival in the US. You will be going through customs when you are tired and you'll still have a connecting flight needed to get you to New Orleans. It helps if you have someone you know pick you up but still, you'll want to make sure it is convenient for them too, versus the middle of the night which is what some of the flights will offer.
Since it is your first time, you might not be comfortable booking a round trip out of Rome since you'd have to have another form of transportation by train to Venice and then have a taxi to the hotel when you arrive and you are overtired from the overseas flight. Check on Google to see what kind of options there are by first looking at roundtrip out of Rome to see times & prices & decide if you want to handle a train trip after the long flight to get to Venice:
Flight out: MSY (New Orleans International Airport code) to FCO (Rome's airport code)
Return Flight: FCO to MSY
Next check the flights that go directly to both your start and stop cities by not choosing the roundtrip or single trip but the multi-city option. As a novice flying overseas and alone you may just wish to go directly to your specific cities:
Flight out:VEN (Venice's airport code) to MSY
Return Flight: FCO to MSY
If you are not seeing good options that get you what you want, you could just see what the best flight options are out of Atlanta for going and returning and book your New Orleans flight separate but you should be able to do this as one trip multi-city.
Some of these airports on return flights out of Italy have 6 AM as a choice. Think about if you need to be at the airport 3 hours in advance, now add the time it will take you to get there, you will be leaving your hotel very early (in the middle of the night). You might want to keep that in mind. There are very few flights that have a decent leaving and returning time since that later in the morning or afternoon you leave, the later it gets in the US so keep that in mind, too. Best wishes. It might be a good idea to connect with the gal from your city that offered her expertise since she's flown out of your city in the past. Best wishes.
