Brothers Karamazov I read off and on for about a year, and it was so worth it! But it's definitely heavy reading. If you're not into long, drawn out stories with numerous subplots, then I'd recommend taking in Crime and Punishment first. This one took me about two months, rather than a year, and left me with a glowing, happy feeling inside. Not to mention the plot is so tightly knit that Chekov must have left his gun there.
If you think that old authors are dull and dry, rest assured that this is not always the case. Crime and Punishment has what is probably the single most intense scene in any book I've ever come across. You thought the drowning of Sita in Ted Dekker's Blink was intense? Yes, it was, but it didn't leave my heart pounding for half-an-hour after I finished reading it.
If Dostoevsky's dry in some way, it's his sense of humour. I don't recall much from Brothers Karamazov that made me laugh, but Crime and Punishment had me giggling on the C-train a few times. For example:
"Blood was flowing from his heart and face; his face was crushed, mutilated and disfigured. He was evidently badly injured."
As if we needed the clarification, thanks. Plus, the character of Razumihin is an excitable, but loveable nut, if a bit dense. Some of the things he says...
"When I heard of all this I wanted to blow him up, too, to clear my conscience...."
If I ever get a dog, maybe I'll name him Razumihin. Not because I mean to demean the character (it'd be an honour for the dog) but because I don't think a non-Russian human kid could pull off "Razumihin". And don't freak out, we could call the dog "Raz" for short.
Naturally, since it's Dostoevsky we're talking about, the book is chock-full of psychological and sociological musings. It explores morality and criminality, which is no surprise. It's not as theological as Brothers Karamazov, but does take a turn in that direction in the last few pages. And I seriously couldn't judge how the protagonist was going to end up in the end, unlike the vast majority of modern stories. You'll have a hint if you read it, since you've read this post first, but I don't think I've given away any spoilerish specifics to actually damage your enjoyment.
Actually, it's this uncertainty about the fate of the characters that makes Dostoevsky so appealing, in my opinion. Most often, characters are painted as either good or bad. Sympathetic bad guys turn good, and any good guys that turn bad do so primarily as a result of awful circumstances, or weren't ever truly good to begin with. Dostoevsky doesn't do that. A character goes downhill because of his or her psychological and spiritual condition. The characters create their stories and aren't merely navigating through them.
And rather than tying up all the unsatisfactory loose ends, Dostoevsky is likely to leave the people in their bad situations. Not all the time - sometimes he'll throw in a "and this particular person did improve over time" near the end of the book, but not always. It's a whole lot more realistic than always fixing everything.
For one example, in Brothers Karamazov the love interest of the main protagonist starts off in a wheelchair. As she and the protagonist make plans to marry, she is almost miraculously healed and begins to walk again. She has good relationships with her mother and her fiance, but as she improves physically, she becomes increasingly manipulative and twisted until she's expressing positively horrifying desires. The very last lines about her in the book (which is in a chapter entitled The Hell Kitten) are these:
"And Lise, as soon as Alyosha had gone, unlocked the door, opened it a little, put her finger in the crack, and slammed the door as hard as she could. Ten seconds later she released her hand, went slowly to her chair, sat down, and looked intently at her blackened, swollen finger and the blood that was oozing out from under the nail. Her lips quivered.
'I'm a vile, vile, vile, despicable creature,' she whispered."
Given that the psychology behind self-harm isn't well understood or even discussed much now, it's particularly potent coming from a nineteenth century author. Though I said it already, it bears saying again - Dostoevsky writes intense scenes!
The Idiot is definitely on my to-read list, now.
There are so many good quotes from both books that I don't know which to give you, so I'll pick one from each at random:
"Every person is needed, and who can tell who is needed more and who less?" Grushenka, Brothers Karamazov
"Talk nonsense, but talk your own nonsense, and I'll kiss you for it." Razumihin, Crime and Punishment