If I were to read just one book by Tolstoy and one book by Dostoevsky, which ones should I read?

Although Dostoevsky and Tolstoy did write short stories and novellas, their reputation is based on their novels. Therefore, I'd recommend their long form works if you are willing to spend several weeks (or even months) on a single book.
I suggest reading Crime and Punishment first. Although this book is fairly long, the crime occurs in the opening chapters and the remainder of the story is rife with dramatic tension. Dostoevsky's other novels feature a lot of exposition and plot structures of greater complexity, though they are certainly with reading. Demons is his darkest (and funniest), and The Brothers Karamazov is his greatest.
Tolstoy's greatest works are Anna Karenina and War and Peace. Although both are excellent, the latter is extremely long and features several digressions on the philosophy of history. Therefore, Anna Karenina is a better place to start.
If you are interested in reading Russian literature more broadly, here are a few titles to consider:
Evgeny Onegin by Pushkin. Although Pushkin isn't well known in the West, he is unanimously considered the greatest Russian writer, with a reputation comparable to that of Goethe in Germany and Shakespeare in the Anglosphere. Evgeny Onegin is exquisitely crafted, although the music of Pushkin's verse won't be conveyed in translation.
The short stories of Nikolai Gogol are strange, dark, and hilarious depictions of psychological torment and social absurdity.
The short stories of Anton Chekhov feature compelling characters from all strata of Russian society. Chekhov, the greatest humanist in the Russian literary tradition, is a master of concision, subtlety, wit, and pathos.
In The Master and Margarita by Mikhail Bulgakov, the devil and his entourage come to Moscow in the 1930s to wreak havoc. This colorful and humorous lampoon of politics and religion is a twentieth century classic and a favorite among Russians. Bulgakov's Diary of a Young Doctor (loosely based on the author's experiences as a countryside physician) and The Heart of a Dog (a satire on the Soviet aspiration to transform human beings) are also worth reading.
My favorite Russian writer is Andrei Platonov. His prose is so strange and beautiful that it would well be worth the arduous effort of learning Russian simply to read it. There are, however, excellent translations of his works in English by Robert Chandler. In The Foundation Pit (the chronicle of a true believer's struggle to accept the failure of Communism) a band of misfits attempt to construct a house for the proletariat only to realize that they are digging a mass grave. A collection published by the New York Review of Books under the title Soul features some of the most beautiful and tender stories in all of Russian literature.
In my opinion, the most compelling literary sketches of life in the Gulag are to be found in Varlaam Shalamov's Kolyma Tales. Shalamov spent seventeen years in some of the most brutal concentration camps, and his works are subtler, darker, and more elegant than those of Solzhenitsyn.
Laurus by Evgeny Vodolazkin is a modern work that may well enter the Russian literary pantheon in time. It tells of the journey of a healer through medieval Europe as he struggles with the eternal and accursed questions of human existence, including love, loss, faith, doubt, sin, and redemption.
Lastly, I'll recommend the works of Svetlana Alexeivich, compilations of eyewitness accounts of the great catastrophies of in recent Russian and Soviet history (including the Second World War, the Afghan War, the Chernobyl nuclear disaster, and the collapse of the Soviet empire). These stories are as shocking and moving as anything in Russian literature, and are (in my opinion) the best means of acquainting Western readers with the souls and struggles of ordinary Russian and Soviet people.

Master and Man is particularly powerful if you live(d) in a place with particularly harsh winters.

I do recommend the novel route, but if you're truly interested in dipping your toe in the waters of Russian novelists, I highly recommend "A Swim in the Pond in the Rain" by George Saunders. It's basically a 300 pg. version of his Russian Short Stories class at Syracuse's MFA program, that has five short stories accompanied by an essay about what he teaches in each of them. Master and Man is one of the stories.

Why not read BAD reviews of these two classicists. Bad reviews will be far more honest and accurate than glowing. Old school novelists are generally terrible due to lack of effective editorship.

Grisham and modern writers can outwrite them anyday.

Christ Almighty. I read to be enthralled by an actual story.

Humanism? Humanism? Humanism? In most best Jim Mora imitation (playoffs?).

secks123r

IMO, The Brothers Karamazov is one of the greatest novels ever written. So much going on at so many different levels with so many different characters.

FWIW, if I were Dmitri I would have just married Katerina Ivanovna (good-looking and well-connected family). Why get all hot and bothered by the femme fatale Grushenka?

I would recommend "The Cat in the Hat" and "Where the sidewalk ends". Both are classics.

I agree with the first answer.

The Brothers Karamazov

Anna Karenina

I also agree. I read those books for the first time not that long time ago and loved them.

I'd also add War and Peace by Lev Tolstoy and Crime and Punishment by Fyodor Dostoevsky

I came to the Russian classics fairly late, maybe in my mid40s. I was pretty widely read before that, having devoured plenty of popular literature along with a decent chunk of the English classics. I had tried and failed to make it through Hugo’s Les Miserables (in the original French) and Cervantes’ Don Quixote (a good translation; perhaps like Dostoevsky I should have learned Spanish to enjoy it in the original), but I’ve loved plenty of classics, with Thomas Hardy’s work coming to mind. Other great English books that jump to mind include Vonnegut’s Slaughterhouse Five and Heller’s Catch-22. I’ve also enjoyed Voltaire and Kafka. I offer these notes as context, since taste is personal, and if what I’ve enjoyed doesn’t resonate with you, you might not like my Russian suggestions.

So, even though I’m reasonably widely read, for me the greatest books I’ve read are War and Peace and The Brothers Karamazov. They are both great novels, vast in scale and scope with interesting characters and plot lines. But each book also contains deep philosophical reflections; W&P on how history gets written, and BK with compelling arguments both for and against the existence of god.

If you enjoy any single book by either author, treat yourself to several by each. Good luck!

I think it would be Leo Tolstoy: Anna Karenina. But in any case, thank you for describing everything in such detail.

It’s wild that the same board that has an intelligent discussion like this on Russian literature can also have a thread asking if doctors are necessary.

It is a year later, but just putting my vote behind these two as well. Karamazov will change your life. So will Crime & Punishment, to be honest. They don't make them like the Russians anymore. Anna Karenina is fantastic and I just finished it last week.

A few people on here mentioned giving up on these books. That is a huge mistake. Pick them back up and finish them. You will thank me (rather, you will thank the authors).

Which translation did you read?

If I had to bet, you read the Constance Garnett version? Virtually unreadable..

Try again with Pevear and Volokhonsky

The thing about the Constance Garnet translations is that the English is somewhat outdated...kind of Dickensian... however, Constance Garnet was a personal friend and correspondent of Tolstoy, so one would have to think that makes her translations the standard. I believe she also has met Dostoevsky as well.

As for recommendations, I recommend Brothers Karamazov. It's a very long book, but it's the greatest Novel ever, in my opinion. Truly rewarding and transformative. I would say The Idiot is my second favorite, but can't go wrong with Crime and Punishment.

I haven't read much Tolstoy, but honestly, I would say if you want to start anywhere in Russian literature, try Dead Souls by Gogol. He's the OG Russian novelist. Dostoevsky wouldn't exist without him. Dead Souls is a very entertaining book, and gives you a little context for character types and societal structure in classic Russian literature. That would help when moving on to other stuff.

Also, you might want to read about patronymics, matronymics, and diminutives. Confused me for a few chapters when I first started reading.