First, the best textbook on Russian history is Riasanovsky’s A HISTORY OF RUSSIA. I don’t know the current edition, which seems to have been revised by another historian, nor do I know the first five, but the previous two were both good.
The question whether to Westernize has been central to Russian intellectual history since Peter I (“the Great”). Peter was a Westernizer, and he wrenched his kingdom’s elite westward, chiefly via an attack on the Orthodox Church. See Anisimov and Alexander’s THE REFORMS OF PETER THE GREAT, for starters. If you really love the topic, Massie’s PETER THE GREAT is excellent as well.
The medieval period in Russian history is usually said to be everything between the Verangian settlements of the 9th century and the coronation of Peter I. There is a FABULOUS collection of the primary materials on medieval Russia: Zenkovsky’s MEDIEVAL RUSSIA’S EPICS, CHRONICLES, AND TALES. It has EVERYTHING: the Primary Chronicle, The Lay of Igor’s Campaign, The White Cowl, Vladimir Monomach (a really great Grand Prince), etc., and it’s CHEAP. If you read it attentively, you’ll understand both the history of Russia and the Orthodox Russians’ sense of their country’s place in God’s Providence. (“The first two Romes have fallen, ours is the third, and a fourth there shall never be.”) For a contemporary summation of that argument/worldview, I recommend a work by my favorite writer: Dostoyevsky’s DIARY OF A WRITER.
If your tastes are more contemporary than medieval, a good collection is the one I was assigned as an undergraduate in Sidney Monas’s course “Russian Intellectual History: From Peter to Lenin”: Raeff’s RUSSIAN INTELLECTUAL HISTORY. This little book is particularly good regarding the fierce 19th-century dispute between Slavophiles and Westernizers (which is the subject 18-year-old Gutzman chose for his term paper). If you want to get the flavor of that debate from a literary source, read Turgenev’s little novel FATHERS AND SONS. If you’re like me, a little Dostoyevsky, a bit of Turgenev, Vladimir Monomach, etc., and you’ll never want to plod through Thoreau or Hemingway ever again. (Of course, Dostoyevsky’s THE POSSESSED is on a similar subject–and is unmatched. However, it’s a bit longer than Turgenev, and I’m trying to lure you into reading about Russia gently.)
The reason that Russia isn’t considered “Western” in “Western Civ.” courses is that “Western Civ.” courses are typically histories of the Roman church and its provinces. They just assume the validity of the Catholic Church’s account of Charlemagne’s coronation in AD 800, the Papal Claims, etc. To mention Russia (not to mention Byzantium) would, shall we say, complicate the narrative.
Russia was my Outside Field in graduate school, and Eastern Christianity was my Outside History Field. I served as a teaching assistant in a 20th-century Russian history course at UVA one semester. Besides that, I know all of the Orthodox services in Greek and in English, and I once published a journal article on a topic in Orthodox theology. If you desire more suggested readings, etc., just ask.