Start with the texture
The Time Traveller's Guide to Medieval England · Ian Mortimer (2008)
Written in the second person and the present tense: what you would smell, eat, wear, pay and die of in fourteenth-century England. A gimmick that works, because it forces Mortimer to answer the questions ordinary readers actually have and academic history usually skips. The best possible first medieval book.
Then the structure
The Inheritance of Rome · Chris Wickham (2009)
400 to 1000, the stretch everyone else calls dark and skips. Wickham's argument is that the post-Roman world was not a ruin but a set of successor states solving Roman problems differently, and he has the evidence. Dense, unglamorous, and the book that will most change what you think the period was.
The Making of the Middle Ages · R. W. Southern (1953)
Seventy years old and still assigned, because Southern wrote about how medieval people thought rather than what they did. Short, elegant, and concerned with the eleventh and twelfth centuries when most of the institutions we inherited were being invented.
Then the disasters
A Distant Mirror · Barbara Tuchman (1978)
The fourteenth century, plague and war and schism, tracked through the life of one French nobleman so the calamity stays human-sized. Tuchman was writing partly about her own century and says so. Historians quibble; it remains one of the most read history books of the last fifty years, and deservedly.
The Crusades · Thomas Asbridge (2010)
Two centuries of holy war told from both sides, with the Islamic sources given equal standing rather than a chapter. Asbridge is good at the uncomfortable part: how ordinary religious conviction produced what it produced.
Then one village
Montaillou · Emmanuel Le Roy Ladurie (1975)
A Pyrenean village reconstructed in extraordinary detail from Inquisition interrogation records, because the inquisitor was thorough and the transcripts survived. Sex, shepherding, heresy and gossip among people who left no other trace. The single best demonstration that medieval peasants had interior lives.
Fitting the Middle Ages into a real life
A thousand years is a long commitment and the standard failure is starting with a survey too dry to finish. Mortimer first, then daily portions to keep the chronology warm: 365 Days of World History (ours, flagged) runs one day in history per day, medieval Europe included, and the world history shelf holds the single-volume overviews. Rome's end is covered on the Roman shelf.
Common questions
What is the best medieval history book for beginners?
Ian Mortimer's The Time Traveller's Guide to Medieval England. It answers the questions you actually have, in order, and it is genuinely funny.
Were the Middle Ages really the Dark Ages?
No, and Chris Wickham's The Inheritance of Rome is the book that dismantles it. The term survives from Renaissance writers with a case to make about themselves.
What is the best book on the Crusades?
Thomas Asbridge's The Crusades for a single-volume account that takes the Islamic sources as seriously as the Latin ones.
Where should I start if I only care about medieval daily life?
Mortimer, then Le Roy Ladurie's Montaillou, which reconstructs one village from Inquisition records and reads like a novel that happens to be true.