The Monogatari series is a set of stories which makes up an overall story.
And it is this overall story which is highly praised as the Monogatari series.

First, I should give my ratings of all the stories individually presented in the Monogatari Series: First Season.

Bakemonogatari: 7/10
Kizumonogatari: 9/10
Nisemonogatari: 8/10
Nekomonogatari: 9/10

Now to critique the story, characters, and writing style.

The individual stories can be divided into parts of 2 types.
Idle Conversation, consisting of Araragi talking with a girl over idle matters.
Action, parts that progresses or brings an end to the story; consisting of fight scenes, Oshino Meme giving lectures, and resolution to the story.

The main problem I had was with the idle conversations. The silly conversations Araragi had with the other characters; on some parts I couldn't fully grasp the joke because of its cultural nature, and on others I simply couldn't find it funny; most of the word plays also turned out a little stale.
An important thing to note here is that I believe these problems mostly arose because I read the translated version (the official English one). As people often say, "The Monogatari series can never be properly translated"; the intricate word plays of the Japanese language that Nisio Isin does and the cultural parts of the book are what makes it so difficult to translate.
But as I kept reading and reading, the silly jokes and unique conversations that Araragi has with the character started to grow into me; and I ended up liking them by the end of the 5th book.

Now the best part of the Novels, the action parts.
Monogatari series has some of the best fighting scenes I've read. They are very well portrayed, and has the perfect pace and intensity.
Oshino's lectures can sometimes get a bit confusing because of all the cultural and language parts (Kanji characters and stuff), but overall they can be understood by the end.
All the stories itself here are good. Some of them can be very simple, but its the simplicity which makes them good.
It's easy to get confused and question the past of some characters, that's because the novels are not in chronological order. You shouldn't think too much about the parts that you don't know, and enjoy the main story that the book is telling, because little by little the series reveals everything.

All the characters here are unique in their own way and most of them are pretty interesting.
It's a character driven story, so you can expect there to be good characters. And by the end you could find a character you very much like. (Meme's my favourite so far)

And lastly, I presume you already probably know, Monogatari has very good writing.
No problem with the conversations and understanding who's talking when (as with a lot of other Light Novels).
Also uh, I'll add that the translation was done really well too; I didn't find any grammatical problems or weird lines.