If I could upvote what Dorothea said 100 times (especially the second paragraph) I would.

Also, I think everyone realizes, no matter what your goals, that <em>some</em> amount of MSA will be useful, I think the question is just one of how much you should concentrate on it at the early stages of your learning.  The thing is, especially in vocabulary related to the so-called "hard" and "soft" sciences, since there's so much vocabulary shared among the different variants, the more varied your vocab becomes the more MSA you'll learn anyway, and most adults are going to wind up speaking something like what's called Educated Spoken Arabic.  The question is more of where do you put your focus at the beginning.  Sham is 100% right, everyone who learns a language most likely wants to know more about the culture, and books and shows are a BIG part of that (soome shows aren't in MSA though), but interaction with people is another big, maybe even bigger, part.  To do that naturally you need a variant (I say variant instead of dialect because by most linguistic standards Darija and Shami, for example, are different enough to be separate <em>languages</em>, whereas Lebanese and Syrian would be more like <em>dialects</em> of Shami, just using the commonsense test of "does Person A use words and grammar that are meaningful to Person B?"  So Darija and Shami can be different languages from each other while being variants of MSA).  Some part of various Arabic-variant speaking cultures will be held in literature, absolutely, but the enormous parts that are held in daily interaction need something else (and the variant is part of the culture, too).  People in Chad and Oman and Lebanon may all speak MSA if they have to (bearing in mind again it's no one's native language) but they all have different cultures, and those are expressed through daily interactions with people.

It depends on their interest..most people start by learning Fusha, and then start learning a dialect...but obviously when their principal goal is to talk to people or to travel to Arabic-speaking countries it will make more sense to learn the dialect (especially in Egypt where communication in Fusha is impossible). 
I think that a big advantage of learning Fusha first is that there a a lot of books teaching grammar, vocabulary etc. There are of course also language books about the dialects, but often their methodological and linguistic approach isn't very good...though there are exceptions :)
I also noticed that many Arabic teachers are better when teaching Fusha than ammiya, because they think that the dialect's grammar is obvious, which it certainly isn't for foreigners... 
I think that the most important thing in the beginning is to learn either fusha or ammiyya, and don't mix the two, which usually leads to confusion...just my opinion :) 

Hello,

Just adding my views to the discussion since I have been thinking a lot about this.  Like Dorothea I agree that it depends on the person's goal. 

For me, I want to be able to read and write Arabic, hopefully as beautifully as my Arabic friends can someday so Fusha is much more important to me.  My opinion then is that anybody with a goal of wanting to be able to read (newpapers and books) proficiently should focus on Fusha - and be prepared for the challenges that come with it! :)

So I think you need to ask your student, do they want to read / write / speak, or just speak?  If they want to speak, then perhaps it is better that they just focus on just dialect.  They will still need to learn the basics like the alphabet and grammar so they can learn new words. 

Whatever it is, I agree 100% that it is better not to mix because it will be very confusing. 

every arab country have a city's and every city have a dialect how someone learn one kind of dialect can understand ether dialect? but if someone learn standard arabic then he can communicate with every one even the arab kid can understand standard arabic when someone talk with him so learn dialect depends on the reason, but if anyone learn just a dialect then we called him "illiterate" someone who lacks literacy, or skill in writing and speaking. so if you don't know to read and write and understand Standard Arabic You will not able to understand the news or newspaper or financial transactions I don't think there anyone learn the language of a country doesn't want to know more about the culture, and the knowledge it's of books and shows that are being said at fusha.
so learn a certain dialect linked with fusha its indispensable

Michael is right. "useful" here really depends on what you want to do with Arabic. If you want to travel and talk from the beginning, then a dialect is certainly more useful. 
If you want to learn Arabic in an academic setting and to read books and newspapers, it makes more sense to start with Fusha, and then learn a dialect.

Doesn't really have to do with this discussion, but I must say that I'm somewhat annoyed by all the native Arabic speakers who say that Fusha is the "right" Arabic and dialects "don't have grammar". The Arabic language history is too long and complicated for such simplifications (and please - every language that's spoken has a grammar). :)