As a Russian I can tell you: don't go there. You won't understand Dostoevsky fully without growing up in the Russian culture, full of depression, fatalism and похуизм (I don't give a damn attitude). Reading classic Russian literature is the right way to depression and craziness. Just don't do that.

I've read my fair share of Russian literature, and I never felt depressed from it. If anything works like the Notes from the Underground or the Overcoat reassured me of my sanity in the face of an irrational society and have often confirmed long held yet elusive suspicions I had on how people actually think or behave.