Don Quixote by Miguel de Cervantes is the obvious starting point — and not just as homework. The novel is set in La Mancha, and reading it before or during a visit here gives the flat, windmill-dotted landscape an entirely different resonance. Cervantes never named the village his hero came from ("a village in La Mancha whose name I have no desire to recall"), but the landscape he describes is recognisably this one. The Penguin translation by John Rutherford is a good modern version.
Homage to Catalonia by George Orwell does not cover La Mancha specifically, but it is the essential book for understanding the Spanish Civil War that tore through these towns and villages in the late 1930s. Orwell's honest, first-person account of fighting on the Republican side gives weight to the war memorials and divided memories you will encounter across Castile.
Spain by Jan Morris is a portrait of the country written in the 1960s and revised in subsequent decades. Her chapter on Castile captures the austerity and grandeur of the plateau better than most travel writing. It ages unevenly but the core observations still hold.