The Brothers Karamazov is not as famous as Crime and Punishment, although it is probably more important philosophically, its themes referred to throughout various essays. Two examples that come to mind are the Sartre paraphrase "If God is dead, then everything is permitted" (attributed to Dostoevsky as a quote but Sartre said it this way, not him) and the story of a boy being mauled by a dog - the "is this evil necessary?"/god existence dilemma.
These two examples are both presented in the story through Ivan Karamazov, and indeed, Camus refers to Ivan throughout The Rebel. A particularly nice (Camus) quote is "All the truth in the world is not worth a child's tears" - Ivan's level-headed philosophy, which Camus believed represented the real views of Dostoevsky.
So there is all that to bear in mind - the story is beautiful. It is a big book, however it is very enjoyable to read, and one sees elements of this story arise in other literature. The court case, of patricide (perhaps alluded to in The Outsider) is particularly enthralling, although it is perhaps just an excuse for Dostoevsky to write long showy speeches.
The three brothers, quite shamelessly manifest the heart, the mind and body. Alyosha (the heart) is such a beautifully innocent character that one can't help but admire his goodness. Classic Dostoevsky trademarks are present, in particular the madness which consumes Ivan (madness is a necessary consequence of all Dostoevsky's characters who cease to believe in God... not to be confused, although reminiscent, of Nietzsche's madman).
Finding a good translation, I think, is important. Some of the sayings, e.g. "One reptile will devour the other" must have quite a bit of room for interpretation, another translation reads "Viper eats viper..." and one American book I read was filled to the brim with the word gotten.
Whilst I enjoyed this book far more than Crime and Punishment, if recommending one or the other, I would probably defer to Crime and Punishment. It more clearly executes an idea that is important historically, whereas Brothers Karamazov is more a nice story with a few philosophical side-investigations.
