Just did that exact itinerary on my honeymoon - flew into VCE and out of FCO. We picked up a car from Hertz on our last day of Venice... drove (and kept car) through Florence... and returned car upon arrival in Rome. Driving between cities was no problem.

Issues:
* Car was about $650 for a week - but wanted an automatic, and that was an issue - need to reserve in advance. Impacted price.
* Traffic in cities was much more difficult than between cities - driving for a few minutes in Rome was intimidating. And I'm used to LA traffic.
* Parking in Florence was VERY expensive - $250 for 3 days.

Didn't take the trains... so can't offer comparison... but apparently trains are difficult with a lot of luggage...