The charters that go to Puerta Plata are probably the cheapest but you will have a very limited luggage (20kg) + need to go by bus to Santo Domingo - best would be Metro from Puerto Plata, Caribe Tours start in Sosua but make lots of stops coming into Santo Domingo. We have used charterflights.co.uk in the past with no problems.
As we need to go to Santo Domingo we usually go with American Arlines these days as the price difference is not that great + we can stay in NY. The main problem with this route is you would have to stay overnight at JFK to get to Santo Domingo.