Having seen many countries by bus & train and then by car, I can only recommend that the personal experience is much superior when you rent a car. Take the advice volunteered above -- always be on the alert (yes, the country is full of one-way streets with people driving the wrong way!). You need to be on the defensive always.
Also, ask, ask and ask. Even if you have a good map, ask and ask. I have yet to have a DR map that has all the right towns on it. Every time you get to a place, ask to make sure you are in the right place. People are friendly. If you are lost, you can always hire a motoconcho/taxi to drive in front of you and put you on the right track.
Do not rent a car to drive in Santo Domingo, though. Too complicated with all the one way streets.
And yes, rent from a reputable company like DR1 sponsor, National (
http://www.dr1.com/national) and purchase all the insurance they have available, and you will be fine.
By the way, in all my travels I have taken this same advice and purchased all the insurance available.