absolutely no point in going into the city as cars are banned from everywhere but the big parking lot at P. De Roma next to the railway station - you'd just have to turn round and drive back down the causeway
I'd definitely take the train - there are all sorts of types and fares but they are cheap cp UK and if you use the DeutscheBahn website they list them all - you can then book on Trenitalia
Book a car locally if you need it but leave the long distance stuff to the Fangio's of this world