Here's another vote for planning an open-jaws (multi-city) trip, where you fly into one city and out of another. Even if the air fare is a bit higher, you save on travel time and transport time, in not having to travel back to your arrival city.
Is 15 days ample? I could make a joke about a year in Italy not being enough, but very few of us can afford to vacation for a year in Italy! I would also suggest to think of your trip in terms of the number of nights, not days. It makes it easier to plan.
In spending time in Rome, Naples, Venice, and Florence, it depends on what you want to see and do. For example, if you love Renaissance art, then you might want to spence 4 nights (three full days) in Florence.
Six days/nights in Rome is good, especially if you want to see the sights of ancient Rome.
I love Rome and Venice, and would add at least one night to Venice. Let's say you have three nights in Venice, that's only two full days. Venice, I think, is the type of place to spend time just wandering around the "streets," and spending time at cafes watching the people (and the boats, if you're on a canal). (I like Florence for its art, but I don't think it's as beautiful a city as Venice or Rome.)
I have never been to Naples, so can't speak to that, but when I visit, I will spend lots of time at their museums, where a bunch of Pompeii artifacts are located.
Enjoy your trip!