You do know that with a fiancee visa he has three months to visit and you either have to get married or go back? I've never actually heard of anyone going back, but it might make other types of visas difficult in thefuture (just a guess). Usually the question is, "should we get married in the DR or try for a fiancee visa". Seems like your question is just for a visit, and immigration frowns on getting one kind of visa with other intentions . . . .
Getting a tourist visa depends on his circumstances, his income, his property etc. Knowing you or being engaged to you may may not matter much.
Nothing is fast, and I doubt the cost is much different in the end.
Patience, patience, and more patience is what is needed either way.
Wishing you the best of luck, and welcome!
(I'm assuming you mean to the US where we live for faster and cheaper