The Caucasus: An Introduction by Thomas de Waal (2010) — De Waal is the best English-language writer on the modern South Caucasus. This short, lucid book covers the history, the conflicts, and the character of Armenia, Georgia, and Azerbaijan together. Read it before you go and the landscape will mean more.
Edge of Empires: A History of Georgia by Donald Rayfield (2012) — Ostensibly about Georgia, but the South Caucasus has always been one tangled history, and Rayfield's deep knowledge of the region illuminates Armenia just as much. Dense in places, but authoritative.
Black Garden: Armenia and Azerbaijan Through Peace and War by Thomas de Waal (2003) — De Waal's earlier and longer book on the Nagorno-Karabakh conflict. Understanding this conflict is close to essential for understanding modern Armenia — it shapes everything from politics to the national mood. Sober and fair-minded.
Armenia: Travels in the Land of Noah by Nicholas Holding (Bradt, 2011) — A conventional travel guide rather than narrative, but Holding writes well and knows the country. Useful for practical context on sites like Sevanavank.