Wild East: Travels in the New Mongolia by Jill Lawless is the best place to start. Lawless was editor of the UB Post, Ulaanbaatar's English-language newspaper, in the 1990s, and writes from inside Mongolian society during the turbulent post-communist transition. Vivid, sharp, and affectionate.
Hearing Birds Fly by Louisa Waugh is a memoir of a year spent in a remote Kazakh village in western Mongolia in the early 2000s. Honest, sometimes uncomfortable, and a genuine account of nomadic village life rather than a tourist's journey.
The Secret History of the Mongols is the oldest surviving Mongolian literary work, written shortly after Genghis Khan's death. Various translations exist; the Urgunge Onon translation is readable and well-annotated. Essential background for understanding why the Mongols see their history the way they do.
Genghis Khan and the Making of the Modern World by Jack Weatherford is the best popular history of the Mongol Empire. Weatherford spent years living in Mongolia and writes with genuine sympathy for both the destruction and the achievements of the empire. Revisionist in useful ways.
Dinosaurs of the Flaming Cliffs by Michael Novacek recounts the 1990s American Museum of Natural History expeditions to the Gobi Desert. Good preparation if the Bayanzag cliffs and fossil sites are on your itinerary — and they should be.
The Desert Road to Turkestan by Owen Lattimore, first published in 1928, describes an overland journey by camel caravan across Mongolia and Central Asia. Dated but evocative — it captures a Mongolia that has changed almost beyond recognition.