The first printing in hardback of course, but you'll need to get your checkbook out for that one. If not that edition, any post 60s edition will tell the same basic story. You don't have to be limited to one edition either. You can get multiple editions for the different artwork if nothing else. No 'modern' revision edition will noticeably alter the story and only a hardcore maven would even notice any differences.
Here's what Wiki says about the different revisions:
In December 1937, The Hobbit's publisher, Stanley Unwin, asked Tolkien for a sequel. In response Tolkien provided drafts for The Silmarillion, but the editors rejected them, believing that the public wanted "more about hobbits". Tolkien subsequently began work on The New Hobbit, which would eventually become The Lord of the Rings, a course that would not only change the context of the original story, but lead to substantial changes to the character of Gollum.
In the first edition of The Hobbit, Gollum willingly bets his magic ring on the outcome of the riddle-game, and he and Bilbo part amicably. In the second edition edits, to reflect the new concept of the ring and its corrupting abilities, Tolkien made Gollum more aggressive towards Bilbo and distraught at losing the ring. The encounter ends with Gollum's curse, "Thief! Thief, Thief, Baggins! We hates it, we hates it, we hates it forever!" This presages Gollum's portrayal in The Lord of the Rings.
Tolkien sent this revised version of the chapter "Riddles in the Dark" to Unwin as an example of the kinds of changes needed to bring the book into conformity with The Lord of the Rings, but he heard nothing back for years. When he was sent galley proofs of a new edition, Tolkien was surprised to find the sample text had been incorporated. In The Lord of the Rings, the original version of the riddle game is explained as a "lie" made up by Bilbo under the harmful influence of the Ring, whereas the revised version contains the "true" account. The revised text became the second edition, published in 1951 in both the UK and the US.
Tolkien began a new version in 1960, attempting to adjust the tone of The Hobbit to its sequel. He abandoned the new revision at chapter three after he received criticism that it "just wasn't The Hobbit", implying it had lost much of its light-hearted tone and quick pace.
After an unauthorized paperback edition of The Lord of the Rings appeared from Ace Books in 1965, Houghton Mifflin and Ballantine asked Tolkien to refresh the text of The Hobbit to renew the US copyright. This text became the 1966 third edition. Tolkien took the opportunity to align the narrative even more closely to The Lord of the Rings and to cosmological developments from his still unpublished Quenta Silmarillion as it stood at that time. These small edits included, for example, changing the phrase "elves that are now called Gnomes" from the first and second editions on page 63, to "High Elves of the West, my kin" in the third edition. Tolkien had used "gnome" in his earlier writing to refer to the second kindred of the High Elves—the Noldor (or "Deep Elves")—thinking "gnome", derived from the Greek gnosis (knowledge), was a good name for the wisest of the elves. However, because of its common denotation of a garden gnome, derived from the 16th-century Paracelsus, Tolkien abandoned the term.
Like I point out, to get early editions you will pay handsomely... if you could even find one. Picking up a 70s or later print addition will hinder you in no way.