Natalie, if you want to read a really brilliant short story about the revolutionary period, then get Yevgeny Zamyatin's "The Cave." It's about an elderly bourgeois couple who find themselves sentenced by the new regime to living like cavemen in the Ice Age. And for an even more imaginative, indeed fantastic version of the Russian Revolution, see Zamyatin's famous novel about a future anti-utopia, or dystopia, We. It inspired George Orwell's even more famous 1984.
Isaac Babel also wrote a collection of short stories, Red Cavalry, about the course of the Soviet war against Poland, which was roughly during the same period of time as the Civil War. It's not my favorite piece of literature, but lots of people admire his work.
If you want me to name my own favorite piece of literature from this period, though, this would have to be Osip Mandelshtam's collection of poems, Tristia (1920) - although his references to the Russian Revolution are understandably pretty oblique, much of the time. See as well the superlative poems of his personal friends and fellow great Russian poets, Anna Akhmatova and Marina Tsvetaeva.
