I agree with the majority here that 3 stops is best. The question then is which 3 and in what order. Since Rome is non-negotiable, that's one down. I'd leave Rome for last . . . it's a busy, bustling city with major sights, not the ideal place to start your first trip especially when you're likely to be in a sleep-deprived jetlag haze. It's also the easiest airport to get to for your flight home.
Venice is my favorite city after Paris, so I would never ever tell you to skip that. It's a perfect place to start an Italian experience. You can ride the vaporetto up and down the Grand Canal and watch the city slip past you, wander the back canals, sip coffee or wine at a sidewalk cafe, and simply soak up the atmosphere. If your other stop is Florence, then Venice > Florence > Rome is the ideal trip. However you might consider skipping Florence and choosing Lake Como instead. Here's where I can't give you much info since I haven't been there yet. It would add a completely different "Italy" - great scenery and what I imagine to be more serenity than Venice (known as La Serenissima, the Most Serene . . . but probably not for its serenity in the past, certainly not in the present). If you choose that, fly into Milan and take the train to Como, then Venice, then Rome.
While Florence is the best place to see Renaissance art (especially sculpture) and architecture, there's hardly a place in Italy that doesn't have lots of beautiful art - Venice has gobs and Rome has more than you can see in a year. Then on your next trip you can concentrate on Tuscany and Umbria. Then a trip to the south . . . Naples, Pompeii, Amalfi . . . and another trip just for amazing Sicily. Darn, Italy is habit-forming.
Ooh, just had another idea. Fly into Milan, stay in/near Como, then Venice . . . but on your way to Rome, leave Venice early and take the train only as far as Florence. Stash your bags at the train station and spend the day seeing the city's highlights (it's all walking distance from the train station), then take a late train to Rome.