I'll start by saying that this is full of spoilers. I don't just mean spoilers about the arc in general, but anything within my knowledge of One Piece might be discussed in this post.
I lied a little bit: Alabasta starts almost with the exact moment the Straw Hats hit the grand line, but there are some other stories that happen before hand that are important.
The first person the Straw Hats meet is a giant whale, Laboon. He might just be the largest animal the manga has encountered. Laboon has a heart warming story that's rekindled much later in the story. Laboon is waiting for some pirates to come back and see him. The specific pirates actually brought him to the Grand Line. He fights the Red Line, the one continuous continent in One Piece. Red Line intersects the Grand Line, and together they separate the world into four quadrants. 50 years have passed and he still waits, despite knowing that the pirates are probably dead. They aren't probably dead, they are dead. We find that out when we meet Brooke, which is how Laboon drives the story deeper.
Alabasta could also be called the Baroque Works arc, because they're somewhat even more important than Alabasta itself. Alabasta is a country ruined by drought and civil war. Yeah, One Piece doesn't fuck around. Basically the heaviest topic it could have is the very first in what I would call One Piece proper. Baroque Works is an underground organization made just to destroy the country of Alabasta and drives the Civil War forward through a series of false flag events.
It's hard to find the true evil person in Alabasta. By the end of the arc, the reader wants both sides to win. There are also many morality events which conflict with different character's views and goals.
Baroque Works sends waves that vibrate the whole story of One Piece. We meet the awesome Bon Clay, and the Straw Hats gain two members during this extended arc, but we haven't gotten there yet.
We shouldn't start in Alabasta yet. The Straw Hats, detoured by Nami's sudden illness, seek out a doctor in Drum Kingdom. During their time on this winter island, many paradigms are carried through. Luffy's determination and strength is cemented, Zoro's resilience is strengthened, and the crew's cohesion proves unbreakable.
Drum is like a mini-Alabasta: the country is ruled by a corrupted monarch, with citizens on the verge of a coup, if only their doctors hadn't been forced away, and a wavering general. Drum's government leaves in cowardice after the Blackbeards invade (this is mentioned just before we find out that Ace is hunting Blackbeard himself). Drum sets the mood by showing that government, especially lead by a monarch, isn't perfect. It sets the reader up to not trust Princess Vivi and her father. Almost anyway, because the reader knows that Crocodile is to blame, but it gives plenty of credit to the rebellion.
The Straw Hats also win their doctor, Tony Tony Chopper, the second Straw Hat with a fruit power. Chopper is also the first non-human member of the Straw Hats, a crew that up until this point remained diversified.
Chopper also represents a common trend in One Piece: the relief of the original five members. By this I mean, up until the Straw Hats met Nami, they sort of just drifted around in a boat, and until they met Sanji, they were lucky to find any food. Nami was the goto medical person on the ship before (a fact hilariously pointed out when she becomes ill), but now there is a doctor. Later we'll see this replacement in CP9 with Franky the shipwright, and somewhat with Brooke the musician in Thriller Bark.
It's almost like, in One Piece each character is a whole puzzle piece but they are also parts of other pieces. Usopp has a passing ability to repair the ship due to his tinkering with weaponsmithing. Nami is a seasoned adventurer, so she has some medical tips. Character's share some traits, but each new member compliments the rest of the crew perfectly. It's an amazing process.
And man, we're just getting started with this arc.