The best advice I can give you is to go for a good quality translation, as a poor translation will completely ruin a novel. The best translator of Tolstoy and Dostoevsky I have encountered is Larissa Volokhonsky, and her translations are widely available (I think she translated my version of War and Peace with Richard Pevear).
I would also recommend reading a biography of Tolstoy before you embark on War and Peace, as his life was fascinating, and I believe it will help you to appreciate certain aspects of his writing in full. The influence of his own life and beliefs is probably most evident in his characterisation of Levin in W&P, as well as much of the philosophy in Resurrection, another of his works that I would highly recommend. As he got older, Tolstoy became increasingly interested in self-denial, and he gave away most of his belongings and isolated himself from his family, before abandoning them completely and dying of pneumonia in the middle of winter at a local train station, where he was about to embark on a life of wandering and introspection.
The major political events surrounding War and Peace are obviously the Napoleonic Wars, so you may want to read up on that a little, but the notes in a good-quality version of the novel will give you a huge amount of information about the historical circumstances. The book is littered with real-life figures to whom Tolstoy gives a voice (for example, Alexander I), as well as many real-life battles and events.
Sorry I can't help you with Gogol or Kafka, but I have limited knowledge of both (although Dead Souls is on my book shelf awaiting me).
Other recommendations I would give are Demons (also published as The Devils and The Possessed) by Dostoevsky, the aforementioned Resurrection by Tolstoy, and The Master and Margarita by Bulgakov, although this is much more contemporary.