The Sun King by Nancy Mitford (1966) is the most readable account of Louis XIV and his court. Mitford was a novelist as well as a historian, and it shows — the book is full of wit and character, covering the building of the palace, the court rituals, the king's mistresses, and the atmosphere of absolute monarchy at its most elaborate. A pleasure to read before or after a visit.
Marie Antoinette: The Journey by Antonia Fraser (2001) is the best modern biography of the queen. Fraser is sympathetic without being sentimental, and the sections dealing with Versailles — the rituals, the isolation, the poisonous court gossip — make the Petit Trianon and Hameau feel vivid rather than merely picturesque. Long but absorbing.
Versailles: A Biography of a Palace by Tony Spawforth (2008) takes the building itself as its subject — how the palace grew, changed, and was used across three centuries, from Louis XIV's hunting lodge to the post-Revolutionary conversion into a museum. Good on the architecture and the individual rooms; useful if you want to understand what you're looking at.
Citizens: A Chronicle of the French Revolution by Simon Schama (1989) covers Versailles's role in the Revolution with characteristic energy. The chapters dealing with the women's march on Versailles in October 1789 — when the royal family was forcibly brought back to Paris — bring the crisis of the court to life better than any narrower account.