You might try "Notes from Underground" by Dostoevsky first, which is much shorter, just to get a taste of his characters and writing style. If you like that, go on to "Crime and Punishment", and then read "The Brothers Karamazov" last.

I saw a dust jacket quote that said something like, "Dostoevsky writes about the unconscious as though it were conscious". When I started reading his books, I felt like he naturally reveals his character's psychology through dialogue (both inner and intrapersonal). They are surprisingly relatable. They have quirks and insecurities, can be hot-headed one minute and fearful the next. "Do you know what it means to demand when you are only in a position to implore?" asks one protagonist. They struggle with big questions, their motivations are laid bare, and they endear empathy as would a self-destructive family member. Dostoevsky may not write inspired literature, but he has something important to say, and he says it from his uniquely Russian soul.