Just speaking for me, one day in Florence is not enough, two days driving in Tuscany or Umbria is ba

If you are willing to do the research you absolutely do not need a travel agent. In fact - unless you want a very luxurious vacation - using a travel agent will cost you more than organizing it yourself.
For your itinerary the best way to travel is train - with possibly a day tour or two from Florence into the Tuscan countryside. This can also be done by car - but renting for only a day or two is usually royal caribbean alaska cruise too expensive.
Your first step is to do some research on the sights you want to see to get an idea of how long to spend in each place. As for hotels, if you give us a budget and your expectations, people can make specific recommendations. And in the spring you may get some negotiable discount rates.
To get open-jaw tickets (into one city and out of another) go to a travel website like Travelocity.com or Orbitz and in the search box check multi-city to get a form that will allow you to get that kind of tickets. Most people recommend flying into Venice and out of Rome on your itinerary, as early morning flights out of Venice are hard to get to because of difficulty with early morning transportation to the airport.
You have twelve days on the ground, so plan for a full day's recovery from jet lag at the beginning. You do not need a car. You can take the train between the three cities, and a train or bus from Florence to Pisa or Lucca or Siena for side trips. A car is obviously unusable in Venice and parking royal caribbean alaska cruise would cost 25 a day. You cannot drive into central Florence, Siena, or Lucca because of traffic restrictions on non-resident autos. Traffic and parking in Rome are insane, so a car is not useful royal caribbean alaska cruise there, either.
If you stay in one place 3 days or more you can usually rent an apartment royal caribbean alaska cruise (a studio would work for you) which will give you more room and a mini-kitchen for less than a hotel room. The drawback is that you have no access to help from a concierge or hotel staff for travel assistance. Look at sleepinitaly.com or VRBO.com for apartments. Or you can look for B B's.
The best time to go is spring or fall, your choice. How long in each place depends on your interests. But be aware that Rome is huge, and packed with things to see. (We are going for the fourth time this fall, and I have only touched the surface of it so far.) So three nights in Venice, four in Florence, and the rest in Rome would suffice, I think. You don't have time for any more places.
You should stay in the historic royal caribbean alaska cruise center of each place, not out of the way somewhere. You won't want to spend precious time each day just getting royal caribbean alaska cruise to the sights, and it's nice to be able to return to your accommodation for a rest in the afternoon if you need it.
3. I'd say 3 to 4 cities/towns are enough for 2 weeks. You say you've read guide books and the internet so you must have a list of things royal caribbean alaska cruise you want to see in each location. What you want to see determines how long you stay in a location. You'll need 5 days to see the major sights in Rome, 3 days for Florence, 3 to 4 days for Venice. That's royal caribbean alaska cruise 11 to 12 days. Use your other 2 days for trips in Tuscany, using Florence as a base. You could visit Siena, Pisa, San Gimignano for instance.
I think Bob the Navigator has an ideal itinerary, as usual. You don't need a travel agent and, as noted above, you can't use a car except for the Tuscan countryside. Trains between major cities are great.
Lots of good advice so far, but I would hesitate to assume you need x number of days anywhere until you decide exactly what you want to see/do. If you plot out your days in Rome, Florence plus a couple of small towns and notice you've already run out of time, you may decide to leave Venice for another trip. Likewise, if you plan to arrive in Venice, would like to visit a smaller town or two (say, Assisi and/or Spello) on the way to Rome and run out of time, leave Florence and the Tuscan countryside for another trip. You could easily spend a week just doing that. The region of Tuscany is 9000 square miles!
Keep in mind that three nights somewhere is only two full days, two nights is only one full day, etc. The day you arrive can be seriously impacted by jet lag, and every time you move from city to city, hotel to hotel, you lose at least half a day.
Just speaking for me, one day in Florence is not enough, two days driving in Tuscany or Umbria is barely worth the effort to rent and return the car, etc. I would rather spend more time in a place and be a little less ambitious, especially on a first trip to a new country.
I am a travel agent, royal caribbean alaska cruise and I would agree - you don't need one unless you are completely unfamiliar with travel planning on the internet. I am planning 2 week Italy trip for someone now and this is my plan for them which they like. (They are too busy to plan themselves and are willing to pay extra for the convenience.)
Before I became a travel agent, I did a month-long trip in Italy, ending in Rome and it was exhausting to finish with such a busy place. i swore next time I'd start with Rome and wind down.... but maybe only 2 weeks won't be so bad.
You could find an agriturismo in Tuscany - a farmhouse (the one we stayed royal caribbean alaska cruise in was beautiful, near Pienza.) It gave us a wonderful experience in the hills of Tuscany. We rented a car while there and visited the villages in the area (there is no public transportation to speak of) and at the end, drove to Orvieto, returned the car, visited that town for the afternoon royal caribbean alaska cruise and finally took the train to Rome. Very easy (except when no one was in the car rental office - she was out having a coffee!)
I agree, Rome was a bit of culture shock for the first hours after the peace and quiet of Tuscany, but we got right into it. We're the same age as you are so I think you'd do OK with that like we did.
You might want to check out my 2011 trip report (sorry it's long, but skip the beginning about Switzerland). We did much of what you are describing so you might get some ideas, and you can see my pictures if you are interested.