Alex,
A few points about using a rental car:
Each driver will need the compulsory International Driver's Permit for driving in Italy. This must be used with your home D.L. and failure to produce one if requested can result in fines on the spot.
Driving will be much slower than using fast trains. Your trip appears to be about 12 days, visiting seven locations. Minimizing travel times will be important.
Many towns in Italy are adopting limited traffic zones (ZTL) to discourage vehicle traffic in historic areas. Inadvertently driving past one of the computerized Cameras will result in a €100+ violation ticket each time.
For such a short trip, fast trains would be a more efficient travel method.
Regarding lodgings, what type of accommodations are you considering? There are lots of good listings in each of the country-specific Guidebooks. In the case of the Cinque Terre, you'll have to decide which of the five villages you want to stay in. March will probably be "quiet" in that area, so Monterosso may be the best choice, as it's the largest town and has the best selection of Hotels.
What type of information do you need concerning food? At least you'll have some home cooked meals when you're visiting relatives in Milan.
Happy travels!