Lenin's Tomb by David Remnick of The New Yorker. Hands down. It's from a verifiable period of USSR history. Much of the very early stuff was/is fraught with propaganda...
Stalingrad: The Fateful Siege, 1942-1943 by Antony Beevor
Stalin: The Court of the Red Tsar by Simon Sebag Montefiore
Moscow, 1937 by Karl Schlögel
The Sword and the Shield: The Mitrokhin Archive & the Secret History of the KGB by Christopher M. Andrew, Vasili Mitrokhin
Iron Curtain : The Crushing of Eastern Europe, 1945-1956
Bloodlands: Europe Between Hitler and Stalin by Timothy Snyder
The Structure of Soviet History: Essays and Documents by Ronald Grigor Suny
Soviet Politics 1917-1991 by Mary McAuley
Red Nations: The Nationalities Experience in and after the USSR by Dr Jeremy Smith
Now, you may also want to read most of what Solzhenitsyn wrote. Not as historical research, most of his stuff is romanticized or novelized. But, he does have a lot of portrayals of Soviet life, which are nice to have as a background.
If you're interested in WWII, I usually recommend Ivan's War by Catherine Merridale. It's a well-researched, fascinating look at how the Soviet Union was affected and reacted to the German invasion and the four years of conflict that followed.
It touches not only on the grand scale of events but delves into the experience at the individual level ─ what life was like for individual soldiers and those behind the front lines.
It really depends on what particular aspect of the Soviet Union you are looking for. There is a huge amount of literature covering the USSR, examining nearly every topic possible, so its difficult to properly give answer without narrowing it down a bit.
Tony Cliff's trilogy Building the Party, All Power to the Soviets and Revolution Besieged is a fantastic, though very detailed and dense work. It's a great explanation for anyone interested in how the Soviet period came about in the first place, why its even called the Soviet period and how revolutionaries demanding democracy could see their dreams "besieged", resulting in Stalin. It takes a very partisan view towards the question of "did Lenin lead to Stalin?" so be warned if "neutrality" is your thing.
Stephen Kotkin's Magnetic Mountain - good mix of the 'straight forward' and more complex and 'revisionist' parts of Soviet historiography.
You should check out the Modern Russian History section on our booklist if you have not already.
Stephen Kotkin's Magnetic Mountain: Stalinism as a Civilization is well worth a read. It's adapted from a collection of diaries that Kotkin himself found, and really gets into the everyday lives and challenges of Soviet citizens during the Stalinist era, discusses (albeit as a matter of factly) Soviet settler colonialism east of the Urals, and gives you an idea of what the Soviet economic system looked like. It's been a while since I read it, but the principle downside is, I'm very uncomfortable about Kotkin's view of people as basically rational and constantly negotiating with a totalitarian system which profoundly effects their lives but not their thoughts or dreams. To me, this surface level analysis is insufficient, and satirically critical Soviet novels of the same era like Master and Margarita by Bulgakov actually do a much better job of getting under the skin of Soviets and exploring small intimacies that are interwoven into the totalizing power of the state.
If you want a good overview of the military, Roger Reese's "Soviet Military Experience" covers the span of the Soviet Union, and Reese is one of the best scholars out there on the subject. It doesn't get deep into any one section, but provides a good overview of the general direction of things.