As I understand it these variants are mostly mutually comprehensible, so you may as well learn modern standard Arabic. The differences come down to pronunciation and the odd extra word.
> a shprakh iz a dyalekt mit an armey un flot
> A language is a dialect with an army and navy
I studied linguistics + Persian as my primary language, but also took Arabic and Kurdish (Sorani) and a bunch of smaller, extinct languages (e.g. Middle Persian, Parthian). I'm a native speaker of Polish so approaching Arabic from the perspective of having learned PL/FA first was quite fun:
We had one exercise where we were given two different pieces of text to translate - the same joke in Moroccan and Iraqi dialects. If you showed them to me without much context there's no way I'd assume they belong to the same language.
But this is an extreme example of course (and my Arabic was terrible then, now non-existent)
(I speak Polish and German, and had a short period when I was learning Hebrew while doing some projects for the Jewish Museum in Krakow ((ages ago, in Macromedia Flash times)). That being said, I'm good at forgetting the languages I studied as soon as I stop using them, be it some weird dialect of Middle Persian or Haskell)
EDIT: https://www.youtube.com/watch?v=yPJIMQS7C5Q and https://karolinacicha.eu/en/sklep/9-languages-2013/
(it's a fun album with songs in 9 languages spoken in that region, incl. yiddish, polish, Tatar, German, Romani...)
I traveled once to Egypt and the tour guide was delighted that I spoke Arabic. We started speaking in Arabic, but after a few minutes we switched back to English because we couldn't form complete sentences without any of us saying "What?".
Morroccan arabic is the most different one as they have strong spanish and french influences so it is less intelligible.