Unless you plan to stay strictly at a resort or do all of your sightseeing as part of guided tours, you'll need a rental car. There is bus service on the island, but they tend to be slow and don't go everywhere.
You most likely won't need a four-wheel-drive vehicle anywhere on the island, so save yourself the money. And while convertibles look fun, the frequent, intermittent rain showers and intense tropical sun make hardtops a better (and cheaper) choice.
Reserve your vehicle in advance, especially during the Christmas holidays. This will ensure not only that you get a car, but also that you get the best rates. Kauai has some of the highest gas prices in the Islands.