I agree with Genistar to a great degree. As I mentioned if your purpose is just to learn 'generic' or 'standard' Spanish, then there is NO need for you to have any dealings with Dominicans or Dominican Spanish. The US is increasingly becoming more and more Spanish, so there is no need to go outside the States to learn Spanish.
However, if a person wants more of a 'cultural' connection (as was expressed by the Poster) then I would recommend learning BOTH 'standard' Spanish and 'Dominican Spanish'. I personally do not feel that you have to learn 'standard' Spanish first. You can just as easily learn both simultaneously. Logically, you can get around just fine only knowing standard Spanish. But, knowing Dominican Spanish is VERY, VERY useful in every day situations. And its NOT a case that Dominican Spanish is 100% slang. There are many phrases and expressions that are not slang in nature, but have much meaning the WAY they are put together.
Learning and knowing the 'native' Spanish of the Dominican Republic will allow you to communicate MORE effectively - and THAT is the objective of ANY language. Its not about impressing someone, its not about being ghetto or uneducated, its about COMMUNICATING EFFECTIVELY. If you are en el barrio, knowing 'barrio spanish' WILL BE useful. If you are in a business meeting, knowing business and formal spanish WILL BE useful. So, basically the more 'types' of spanish you know, the more effectively you will be able to communicate. Knowing Dominicanismos WILL BE useful because nearly ALL Dominicans use them in some capacity. Knowing the COMMON language will allow you to be a part of the culture.
Take English for example, if a person goes to a very urban and lets say 'dangerous' neighborhood, of WHAT benefit will it be for him/her to speak formally?? "oh hello sir, how are you today? Might I trouble you by asking for the directions to the nearest gas station?" If anything, it will be of MORE harm, because it will make him/her stand out as 'lost', 'nieve' and even 'vulnerable'. A simple FLEXIBILITY in language "hey my man, where can I get some gas at?" COULD BE the difference in how he/she is perceived, and that COULD BE the difference in him/her being singled out as a target. Or, imagine a person walking down a street, they immediately draw the attention of the locals as they know EVERYBODY in the barrio, they are being followed by someone from a distance by a local looking to perhaps take advantage of them in some way- perhaps taking them as a tourist, they continue to get close and then the person being followed reacts - saying "disculpa, pero como puedo ayudarte se?or?" in some strong Gringo-esque accents will automatically tell the pursuer "ah, I was right, they must be lost....easy potential target". But if the turn around and say, "pero ven aca!! pero queseto?! que tu quieres conmigo eh?! SUELTAME! oiste?!" then the pursuer will think "oh they must be from around here nearby, or they must have relatives nearby....not so easy a target". Naturally, not ALL situations are that serious or 'life and death' but it highlights the practicality and importance of being FLEXIBLE and being able to communicate effectively. How people perceive you goes hand in hand with how people treat you. So at least having the ABILITY to speak and very versatile spanish will be useful whether its in the streets, at the park or in a business meeting. So I say the more tools you have, the better off you are.