4 Entry Points into the Mad Multiverse of Michael Moorcock

If you’re looking for a straightforward adventure:
Jewel and Amulet
Though not an obious starting point for the Eternal Champion series, the Hawkmoon books are still an engaging read, and self-contained enough that new readers won’t get lost in the references to mythology and metaplot. The Jewel and Amulet follows the first two adventures of Baron Dorian Hawkmoon von Köln, as he leads a resistance against the evil Baron Meliadus and the Empire of Granbretan. While Jewel is definitely darker than most high adventure novels, the hallmarks—a clear-cut hero (arguably the least morally ambiguous Moorcock protagonist), a besieged kingdom, epic battles, and an evil, masked empire—grant new readers definite toe-holds to keep them from getting swept away by the sheer strangeness of Moorcock’s creations.

If you want to start at the beginning:  
Phoenix in Obsidian 
While not chronologically the first book in the Eternal Champion series, Phoenix is a much more readily accessible work than its predecessor. John Daker (a body-jumping man from twentieth century Earth) finds himself in the body of Count Urlik Skarsol, wielder of the Cold Sword, in an ice-bound land watched over by a dying sun. Phoenix in Obsidian explains a lot of the mythology that continues throughout the series—the ever-present Black Sword, the idea that each world and time has its own champion, and the idea that morality has shades of gray all over the place—but none of the bleak nihilism nor outright genocide contained in The Eternal Champion.

If you like mythic fantasy:
The Knight of the Swords
The Corum saga follows the exploits of Corum Jhaelen Irsei, last of a dying race known as the Vadhagh. The Vadhagh have continually lost ground to humans, who have decided to hunt and kill them to extinction. After losing his left hand and eye to human torture, Corum is drawn into a conflict against the evil forces of Chaos (who use the humans as puppets) to restore the Lords of Law to their rightful place of power. While more rooted in tradition than some of Moorcock’s work, Corum’s story spans multiple planes of existence and includes gods, demigods, and elements of older flavor of mythic fantasy. The Corum Saga also explains the cosmology of the Lords of Chaos, Grey Lords of Balance, and Lords of Law, all of which feature prominently in the larger lore.

If you like your science fiction really weird: 
The Final Programme
A bisexual rock star scientist assassin and a ruthless computer programmer attempt to get their hands on the Final Programme, an equation used to create the ultimate supreme being. The Final Programme is the first book in The Cornelius Quartet, the psychedelic adventures of antihero Jerry Cornelius and his associates. Moorcock’s story takes flavor from popular media at the time (The Prisoner, The Avengers, et. al) and pulp sci-fi (Cornelius’s psychotropic needle gun), but mixes in metaphysics, mythology, and his own bizarre flourishes to create a violent and strange but compellingly readable story of weird science and shifting identities in a brightly colored, blitzed-out alternate Earth.
What was your first foray into the Multiverse?