The 1855 edition of Leaves of Grass was the first and the best.
When I was young I bought the big deathbed edition, not knowing about the 1855 one. I became a Whitman disciple. Either version is a good place to start, but the 1855 is the best version of the early poems and a fine introduction to W.W.
The 1855 version was ignored for quite a long time in Whitman studies, but started recieving critical attention after Malcolm Cowley worked to revive it in the 1950's. It was his version that used to be available, until recently, as a Penguin Classic.
So whats the difference between 1855 and the Deathbed one?
Throughout his lifetime, Whitman not only expanded LOG, his only book, with gobs of inferior-- and sometimes truly awful-- poems (especially when he was older) but he also revised many of his early poems for later editions-- revising them almost always for the worse.
The 1855 edition is realtively short and reflects the diminutive, obscure quality of the original. The poems are full of Whitman's original fire before he tinkered with them.
Bloom, the author of the introduction, is in the estimation of many America's best living literary critic. He profoundly knows and adores Walt Whitman.
If you have the slightest interest in reading American Poetry,drop whatever you are reading (unless it is perhaps Dickinson or Emerson) and get this book. It's still America's best. Nothing since has been (and nothing will ever be) better. The only American poets after Whitman who mattered were deep readers of LOG: Hart Crane, Wallace Stevens, TS Eliot, John Ashbury. (A Ginsberg, C. Sandberg, and O. Paz resemble him superficially but they are are wonks.)
If you are interested later in getting all of Whitman's poems, skip all the in-between editions and get the 'Deathbed' Version, which has many good and important poems like 'When Lilacs Last in The Dooryard Bloomed' and 'As I Ebbed with the Ocean of Life'-- as well as many bad ones, to go with your 1855.
The Deathbed Version (Whitman approved it as the final Version of his one book as he lay dying) is probably close to ten times as long as the 1855 edition.
But Whitman got it right in 1855.