Reddit mentions of Media Arabic: A Coursebook for Reading Arabic News (Revised and Updated Edition) (Arabic Edition)

Wall of text incoming:

Al-Kitaab fii Ta'allum Al-'Arabiyya (al-Kitaab generally) is nearly universal for beginning and intermediate Arabic learning in the States. There are three books, and it teaches fusha, which is media Arabic. All educated Arabs are proficient in this dialect, though it is rarely used outside formal settings.

Only one dictionary you'll need: Hans Wehr is the Arabic student's bible. You won't find much use for it off the bat because it's not strictly alphabetical, it's alphabetical by root. So until you learn to spot the root of a word it'll be hard to look anything up. It's also only Arabic-to-English, but al-Kitaab provides more than enough vocab to get you on your feet and Google Translate can fill in gaps (ONLY use Google Translate for individual words, then Hans Wehr to verify; Google Translate will botch sentences).

The most widely understood dialect would most likely be Egyptian, though oddly it is also one of the weirdest/most divergent from Classical Arabic due to Coptic influence. Fortunately, because it's so popular, there are lots of materials out there. That said, probably best to start with fusha, and branch out into dialects after you have a good handle on it. It'll help you understand where a lot of dialectical words come from. Additionally, al-Kitaab has a small Egyptian lesson at the end of each chapter, so you can get some basic exposure without having to functionally learn two languages at once.

Farther down the line, you can get Media Arabic, which is a collection of short articles by topic, with little exercises and loads of really useful vocab. Not strictly necessary if understanding the news isn't in your wheelhouse, but if you're serious about learning Arabic it's a really good intermediate/advanced step.

If you get serious about Egyptian, Pimsleur's Egyptian course is a good jump start, but also not really necessary and hard to do right because of the time commitment. It gets expensive, too, so make sure you're going to use it.

Some of my favorite books for Egyptian come from the American University in Cairo Press:

the Kallimni Arabi series is basically al-Kitaab for Egyptian Arabic. Very useful place to start.

the Arabi Liblib series
gets really into the weeds of how Egyptian speakers communicate. They're basically dictionaries of dialectical adjectives, idioms, and proverbs.

In addition to books, check out Memrise. It's a great vocab tool, and entirely user-generated, so there's a lot of content.

I also like to listen to BBC Arabic Radio. It's 24/7 so you can just pick it up whenever. Both fusha and various dialects. Exposure is extremely important in language learning, and even moreso when learning a language as alien to English as Arabic is.

On top of all this, just putz around on YouTube and Twitter. Arabs are all over social media and it's not hard to get exposure there.

• Pronunciation (any language): Try Alexander Arguelles' Shadowing technique
  
• Grammar: Use a textbook like Mastering Arabic to learn the grammar and practice new concepts. Once you feel ok with a new grammar point, practice what you just learned by writing little essays on Lang-8 - native speakers will correct them for you and it allows you to practice both grammar and vocabulary.
  
• Vocabulary: If you're studying MSA, Media Arabic could help you. There's lots of vocabulary books out there, like this one, or if you want to practice reading as well, this could be of interest
  
  Have a look at Memrise and Anki where people have put entire decks of flashcards to learn vocabulary. That way you can practice during your commute or any free time you may have.

Like I said, filling the gaps is really going to come down to what other resources you have, but from what I've heard and what I've found in my experience you're going to need these resources regardless of which book/course you choose.

Mastering Arabic will take you through the Intermediate level of MSA, roughly. The difference in vocabulary between it and a book like Al Kitaab is significant, but that would be the case with most books compared with Al Kitaab. So you'll probably want to supplement your vocabulary from real world readings, from a dictionary, or from other types of work books. Not that Mastering Arabic leaves out a lot of vocabulary, but each book is roughly 200 pages so there just isn't going to be as much vocab covered as in a college textbook.

The rest of it is really grammar and verbs, for which you'll want to use things most any other Arabic student will use. A good grammar book like the ones I pointed out before, either 501 Arabic Verbs or ACON for verbs, and then anything else you can get your hands on. If you're self-learning, you have to understand that no one resource is going to take you all the way there. I think Mastering Arabic is the clearest book out there, especially for a self-learner, but you're going to need more than the page and 8-10 examples they provide on grammar points.

I think the activity books help solidify vocabulary and some grammar points for me, plus it's just extra practice because you can't learn a language without a decent amount of practice. It's not a bad idea to go without them, but I've found them helpful for the most part.

Here's one of the grammar books I mentioned, and it's one that's highly recommended. The other one I rely on is here. You'll also get a lot of use likely out of the websites arabic.desert-sky.net, GLOSS, and Youtube channels like this one and this one. And that's just scratching the surface. /r/learn_arabic has a lot of great threads and resources available (I saw you posted this there as well), and google is your friend. And after a number of years and a couple of attempts at becoming fluent, the best advice I can give you is to be patient and to practice as much as possible and use what you have available to you.

Once you crack the Intermediate stage, take a look at books like Media Arabic and websites like Foreigncy. But at that point your learning will be mostly done with your dictionary, a grammar book, and things to read/listen to from the real world.

Good luck! Arabic is a beautiful and amazing language that continues to surprise me.