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I'm sure you're more than excited about your upcoming trip. I hope I can help with a couple of answers. Using a travel agent can be of valuable assistance. You should however make certain that he or she has experience with/knows the destination. Unfortunately, many travel agents today or simply computer operators and you don't want one of those. They can assist you with flights, hotels, train tickets, etc. Yes, you probably can do it yourself, but ask yourself how valuable your time is, and weigh that against the cost of using an agent. Travel agents charge a fee which often starts at approx $25 or $50 per person for basic services, (Airline, hotel reservations) and move up from there for complete itinerary planning, more complex travel plans.
Packaged tours, in spite of what some one has said here in another post are often cheaper than doing it on your own. The tour opeartors get preferential rates from airlines and hotels and pass them on to their clients. Packaged tours can offer value for money; you may get more bang for the buck. I myself don't care to spend two weeks or so with a bus load of people I've never seen before, but that's me.
Depending on the cities, you can fly into one place in Italy and home from another. The term the airlines use for those cities is common rated. Let's say Rome, Florence and Venice are common rated. That means you can fly into any of them, out of any of them at no additional cost. You could not however, fly into Rome and out of Milan or Naples at the same fare. Things like this may be something a good travel agent can help you with. I would suggest that you fly into Rome and out of Venice as they are at opposite ends of the country and you don't want to be back tracking. Also, Venice is magical, a great place to end your trip and a lot more relaxing than Rome and I happen to love Rome. You will probably have to connect someplace if you leave Italy from Venice. To the best of my knowledge the only airline with nonstop flights between Venice and the USA (New York City) is Delta.
I would suggest that if you go to Sicily you fly there; go into Palermo and out of Catania or vice versa. Sicily is actually an area you may want to consider driving or using a package tour. Several tour operators offer one week (or less) escorted tours of Sicily. If you opt for driving in Sicily, DO NOT get a rental car until the day you actually leave the city you are in, either Catania or Palermo. Traffic in either city is unreal and you couldn't use a car there any way. Pack you bags, check out of the hotel and then get the car and leave for your next destination. Another word on renting a car; do it before you leave the States, it will be a lot less expensive then getting one locally in Italy.
As for driving, while I love to drive any time, any place, you have to keep in mind that this is your first trip to Italy, there are tons of things to see and do and do you want to spend your time looking out the windshiled for road signs, exits and traffic or seeing the sights? Also keep in mind that gas is almost stupidly expensive, many areas in city centers are closed to cars (central Florence for example) and that parking at hotels is NOT cheap. Another thing to keep in mind about driving in Italy is that the Italians drive MUCH, MUCH FASTER than we do. I'm not saying don't drive at all, just think carefully about it, weigh your options. One of the places you may want to drive a while is in Tuscany. THere are a lot of small, charming towns and cities where a car is the best way maybe the only way to get to them.
I would make hotel reservations in advance. If it were my first trip to Italy, I would not want to wing it, hope I could get reservations at the time of my arrival in a strange city.
I hope this helps. Have fun planning your trip and buona vacanza!