Travel by train between cities is the best option. Rome to Florence is approximately 1.5 hours, Florence to Venice is approximately 2 hours, and Venice to Milan is approximately 2.5 hours. The cost for a one-way train ticket averages around €30-40 per person each leg.
If you have more time, consider adding a day trip to Pisa from Florence to see the Leaning Tower. If you have less time, you can skip Milan and spend more time in the other cities or add a stop in Naples to explore Pompeii.