Okay, Connavar, get ready for a very convoluted ride.....
First, yes, reading that collection would be fine, as it contains the earliest
published Elric tales. But, as I said, you'll probably want to avoid the stories that make up
Stormbringer! until you've read the rest of the series (at least, that would be my judgment, given comments in some of your other posts elsewhere).
Here's the list (first publication dates only given; if a story has been revised, that's noted, but not the date):
"The Dreaming City" (ss) --
Science Fantasy (June 1961)
"While the Gods Laugh" (ss) --
Science Fantasy (October 1961)
"The Stealer of Souls" (ss) --
Science Fantasy (February 1962)
"Kings in Darkness" (ss) --
Science Fantasy (August 1962)
"The Flame Bringers" (ss) --
Science Fantasy (October, 1962) (later retitled "The Caravan of Forgotten Dreams" for inclusion in the latest edition of the Eternal Champion cycle)
"To Rescue Tanelorn" (ss) --
Science Fantasy (December 1962)
"The Last Enchantment" (ss) --
Ariel, the Book of Fantasy vol. 3 (1978) (while not published until this date, the story was apparently written at the same time as the ones listed above; it was later retitled "Jesting with Chaos" for inclusion in the most recent edition of the Eternal Champion cycle)
"Dead God's Homecoming" (ss) --
Science Fantasy (June 1963)
"Black Sword's Brothers" (ss) --
Science Fantasy (October 1963)
"Sad Giant's Shield" (ss) --
Science Fantasy (February 1964)
"Doomed Lord's Passing" (ss) --
Science Fantasy (April 1964)
"Master of Chaos" (ss) --
Fantastic (May 1964) (retitled "The Dream of Earl Aubec" for later printings)
"The Singing Citadel" (ss) --
The Fantastic Swordsmen (anthology) (1967)
The Sleeping Sorceress (novel) -- (1971) (later retitled
The Vanishing Tower)
"The Sleeping Sorceress" (ss version of novel) --
Fantastic (February 1972)
Elric of Melniboné (novel) -- (1972)
"The Jade Man's Eyes" (ss) --
Flashing Swords! #2 (anthology) (1973)
"The Lands Beyond the World" --
Flashing Swords! #4 (anthology) (1977)
"Elric at the End of Time" (ss) --
Elsewhere (anthology), 1981
The Fortress of the Pearl (novel) -- (1989)
The Revenge of the Rose (novel) -- (1991)
"The White Wolf's Song" (ss) --
Tales of the White Wolf (anthology) (1994)
Okay? Wait... the fun's only just beginning.... In the late 1970s, Moorcock did some revisions (sometimes light, sometimes heavy) to all the Elric tales published up to that point, to reconcile inconsistencies, to bring them into line with his growing conception of the multiverse and the cycle as a whole, and to alter emphasis philosophically. This set was the 6-volume set that was so long the standard edition of the Elric series (until the introduction of Fortress in the late 1980s), even though they left out "The Last Enchantment":
Elric of Melniboné (October, 1976)
The Sailor on the Seas of Fate (December, 1976)
The Weird of the White Wolf (March, 1977)
The Vanishing Tower (June, 1977)
The Bane of the Black Sword (August, 1977)
Stormbringer! (November, 1977) (this edition restores nearly a quarter of the work from the original serial, which had been cut when it was first published as a novel)
Thereare, so far as I know, no substantial changes between these and later editions, save that the newer work is now included... except that now, there's a new edition of Elric coming out next year, I hear, which (iirc) brings in some new material he's written since....
Del Rey Online | Elric The Stealer of Souls by Michael Moorcock
And then there's the two Elric scripts that he wrote for Marvel's
Conan the Barbarian (issues #14 and 15) which come between
The Sailor on the Seas of Fate and
The Weird of the White Wolf....
Personally, my suggestion (if you can afford/find it) is to read the two-volume edition of the Elric tales from the Millennium/White Wolf set:
Elric of Melniboné (Am. ed.:
Elric: Song of the Black Sword) and
Stormbringer (Am. ed.:
Elric: The Stealer of Souls), which includes all but the newest of the material in the Elric series proper.
And we're not finished yet, as Elric makes appearances in both the Corum, Hawkmoon, and Dancers at the End of Time series (as well as occasionally, in a lighter vein, in the Cornelius tales); under different names in much of Moorcock's later fiction (such as
Fabulous Harbours), and in an important capacity in three relatively new novels:
The Dreamthief's Daughter (an odd sort-of sequel to
Fortress of the Pearl),
The Skrayling Tree, and
White Wolf's Son. These are more closely connected to the von Bek books than the Elric series, but he does play a major role in them; so much so that they are often considered a new (but separate) Elric series....