If yhou are going to stay in smaller towns, car is much better. Make the reservation before you go, it's cheaper. I recommend Beaulieu sur Mer as an ideal place to stay. Small town, right on the sea, lots of shops and restaurants, though. Even a supermarket. Easy to park on the street.
You can even take the train to Nice, 7 minutes, and Nice has a great new Tram system. Also you will be near to Eze, Cap d'Ail, Cap Ferrat (Don't miss David Niven's House!) and Menton. Monaco as well, (take the train) although we personally do not like Monaco at all.
We've gottten some great rates the past 2 trips on Hertz or Avis through the Delta of AF FF programs. If not already a member, join online instantly.
Also, check these sites out for cheap rentals:
www.novacarhire.com
www.carrentals.com
We never get extra insurance, we are covered through Chase Visa. (most Visa cards have coverage). Liability is through our Homeowner's Umbrella. I had a small accident once (backed into a tree in a parking lot) and never paid a dime.