Michael Moorcock’s Elric of Melniboné is immensely influential. It not only inspired Dungeons & Dragons—especially its intelligent and cursed swords—but also left its mark on numerous books (The Witcher, the Targaryens in Game of Thrones), comic books (Berserk, and probably many of the "multiverses" form Marvel etc.), and even music (Hawkwind, Blue Öyster Cult, both of which collaborated with Moorcock himself).
In short, Elric is one of the pillars of dark fantasy.
Another complicating factor is Stormbringer—the book that (sort of) concludes the saga. It’s one of the greatest entries in the series (probably my favorite), one of the two Elric works mentioned in the Appendix N, and ironically, one of the earliest to be published.
I’m a big fan of Elric, and part of me wants to just say: Read the whole thing in internal chronological order! But I think it’s easier more helpful to offer a few different starting points.
So, how do we begin with Elric?
Start with Elric of Melniboné (1972).
It’s not the strongest novel in the collection, but it’s a solid introduction to the character, his world, and the themes that define the saga
If you like it, you can go on and read The Fortress of the Pearl, The Sailor on the Seas of Fate, and The Weird of the White Wolf, before going to Stormbringer.
All of them are great.
But I'd say is even easier to just pick any collection of your choice, as long as it contains the first and the last.
For example (from Wikipedia):
In 1977, DAW Books republished Elric's saga in six books that collected the tales according to their internal chronology:Elric of Melniboné (Hutchinson, 1972, cut vt [variant title] The Dreaming City Lancer, 1972 US; DAW, 1977) ISBN 0-425-08843-XThe Sailor on the Seas of Fate (Quartet, 1976; DAW 1977), ISBN 0-441-74863-5The Weird of the White Wolf (collection, DAW, 1977, contains "The Dream of Earl Aubec", "The Dreaming City", "While the Gods Laugh" and "The Singing Citadel"), ISBN 0-441-88805-4The Sleeping Sorceress (NEL, 1971; Lancer, 1972 as The Vanishing Tower; DAW 1977), ISBN 0-441-86039-7The Bane of the Black Sword (DAW, 1977, fixup of "The Stealer of Souls", "Kings in Darkness", "The Flame Bringers" and "To Rescue Tanelorn"), ISBN 0-441-04885-4Stormbringer (cut, Herbert Jenkins, 1965; restored and revised, DAW, 1977, Berkeley, 1984, fixup of "Dead God's Homecoming", "Black Sword's Brothers", "Sad Giant's Shield" and "Doomed Lord's Passing"), ISBN 0-425-06559-6
Now, if you dislike it... we have a few options.
You could go from Elric to directly Stormbringer to see what all the fuzz is about. If you like the story but dislike the prose, there is another great alternative: reading the comics.
Elric's comics and graphic novels
Elric has been adapted several times into comic book format. My favorites are the ones adapted by Roy Thomas and illustrated by P. Craig Russell and others—and once again, Stormbringer (by P. Craig Russell) stands out as the best of the bunch, but I'd recommend reading the The Michael Moorcock Library first (Elric volumes 1-5: - Elric of Melniboné, The Sailor on the Seas of Fate, The Dreaming City, The Weird of the White Wolf, The Vanishing Tower).
There is also a French version by Julien Blondel in the works, with a few volumes already published. The art (Didier Poli et al) is both dark and really stunning. But the story is much less faithful to the originals, which I'd favor on a first read.
There are other comics that are also worth checking out (The Making of a Sorcerer, Druillet's version, Moorcock's Multiverse, etc.), but I'd start with the "main books" mentioned above.
Additional reading:
NOTE: Tales of Argosa is the deal of the day, only $9.98 - 60% off ! I'm a big fan of LFG, so I recommend checking this one out! (affiliate link).
Curiously, this might be a decent system to run an Elric game, due to its "dark" undertones and dangerous magic. I have to read it more carefully before I can say for sure!