There is a lot of Rome, most of the centre, where you cannot drive without expecting a very large fine. ZTL is the term to research.
Almost all of Rome's roads are extremely bumpy due to their being made of stone blocks similar to cobblestones, and traffic is extremely heavy, and then you add in the motorinos. Parking on the street is nearly impossible and car silos are very expensive.
I drive my car to Italy most years. I drive all over the north and central and southern areas but there are two cities where I leave my car parked for the full duration - Napoli and Roma.
Follow the advice above.
Why are you being advised to rent a car in Rome? It would help us understand. I'm sure that there is a good reason. Is your visit for business and the company needs lots of heavy things moved around, and can get you out of the fines?