Reddit reviews Colloquial Palestinian Arabic: An Introduction to the Spoken Dialect (Arabic Edition)

For MSA I used Mastering Arabic and it was great; very fun to read and kept me motivated throughout.

Mastering Arabic 1 with 2 Audio CDs: Third Edition (Arabic Edition) https://www.amazon.com/dp/0781813387/

For Levantine Arabic I have these two recommendations, but both are more advanced and expect an existing understanding of Arabic.

Living Arabic: A Comprehensive Introductory Course (Arabic and English Edition) https://www.amazon.com/dp/0974484342/

Colloquial Palestinian Arabic: An Introduction to the Spoken Dialect (Arabic Edition) https://www.amazon.com/dp/0982159536/

I think this book will also help when it comes to Palestinian dialect.

https://www.amazon.com/dp/0982159536/?ref=idea_lv_dp_ov_d

Al-Kitaab is garbo. I've been using Mastering Arabic Grammar by Jane Wightwick and it's much easier for starting with the basics.

IIRC you want to learn Levantine, so you should check out these:

This one comes highly recommended.

I have the Iraqi version of this and it's good for learning phrases.

Also check out Hiba Najem on YouTube if you haven't already, she has a bunch of videos about Lebanese Arabic.

This one is ok if you already know some Arabic.