Personally, I don't agree with the philosophy of "must see Rome, Florence, Venice etc" in one trip. Why not leave something for a future trip? These cities are some of the most worthwhile destinations in the world, it seems a pity to abandon two thirds of the sights in one to rush off to the other.

In general, train is the way to go in Italy unless you want to visit small villages or sights out of town. To visit the large cities train + taxi is convenient and cheaper. Just don't carry a ridiculous amount of luggage!