I think it is simplistic to say that a "newbie" should never drive in the DR. A lot depends on the individual, their experience, and their confidence in their abilities to adapt to new situations. I rented a car on my first trip to the DR, and on each subsequent trip, and have driven all over the country. It demands concentration, and you cannot assume that anyone else on the road will obey laws, including those of common sense. Quite frankly, I feel safer behind the wheel than with someone else driving, but that's just me. If having a car fits your travel plans and budget and you are an experienced and skilled driver, I wouldn't rule it out.
There will be several companies with rental offices at the airport, and this is the most convenient, but there is a daily location surcharge. You will save money if you can get to an office in the city, but that may not be an option in Punta Cana. You can do a search for rates and locations on Travelocity or Expedia.