Best for mostOxford (1922 text) · 1922
Ulysses is hard, and the help matters more than the textual debates. Oxford's edition gives you the original 1922 text with Jeri Johnson's excellent introduction and notes — the context you need to keep your footing. For a first read, that guidance is worth more than the fixes in the scholarly text. This is where I'd start. (Many readers also keep Gifford's separate annotations nearby.)
The scholar's textGabler (Corrected Text) · 1986
Hans Walter Gabler's 'Corrected Text' is the version scholars cite, with the marginal line numbers used in criticism — it rebuilds the text from the manuscripts and fixes thousands of small errors. It also set off one of the great literary feuds: the critic John Kidd argued Gabler introduced errors of his own. Essential for study; light on notes for a first read.
The standard textModern Library · 1961
The Modern Library edition prints the long-standard text that preceded Gabler — the one most readers used for decades. A handsome, reliable reading copy. If you want the familiar text rather than the corrected or the original-1922, this is it.
James JoyceUlyssestr. Free (public domain)
FreeFree (public domain) · 1922
The 1922 text is out of copyright and free — Project Gutenberg and others. Just know that Ulysses without notes is rough going; you'll want a companion guide. Free and complete, best for re-reading or sampling.