I highly recommend you find a copy of the 1984 Gabler edition of Ulysses if you can. It's a large softcover book, full size, w. grey cover, red and blue title on the front, and "The Gabler Edition" as the banner.
This is the "corrected" edition, absolutely the most accurate and authentic edition ever. When it first came out, rumor was that it was a "computerized" edition, whatever that means. It was in fact not.
What was done was to take ALL existing editions and scan them into font recognition. Also scanned were all correspondences between Joyce and the publishers, his changes, their revision, his objections to their revisions, etc. Every possible scrap of text was scanned.
Then a comprehensive comparison was made by computer, listing all the differences. Each was flagged with a footnote showing where the difference came from (1922 Paris 1st printing, 1924 revised, 1926 revised -- all from Shakespeare, Paris. Then the 1934 Random House (US), 1936 Bodley Head (UK), winding up w. a 1961 Random House and a 1968 Penguin, plus several interim revisions.
I myself have the following editions: several copies of the 1986 Gabler (I've always got one in the trunk of my car for "emergencies" ha ha. The 1984-86 Gabler 3-volume hardcover synoptic and summarized version -- this is the one containing all the repetitions and differences, each teeny change flagged as to which edition it came from. A Viking paperback edition, an original 1934 Random House, a 194? Bodley Head, and, treasure of treasures -- a 1924 first edition from Shakespeare & Company, Paris!
Anyway, after the synoptic edition was ready, scholars pored over the differences, researched back into original Joyce manuscripts and correspondence, and verified that some errors had never been corrected. You have to realize the task -- Ulysses is a hugely complex book just on its own. Consider that Joyce send chapter by chapter to the publisher, much of which was typeset my French-speaking printers, and the usual errors crept in. Joyce would fix the galley and send them back, but often that never got done -- Joyce's eyesight was now failing and he was trying to concentrate on The Wake.
Nobody on the Gabler team took liberties. All changes were carefully authenticated via Joyces's earliest manuscripts and his later corrections. Then after careful consideration, the many teeny changes were made and a new corrected version prepared, then reviewed, edited, and rechecked.
Example of a small change: at the Hades chapter (graveyard) Bloom sees or imagines a whiff of grave gas and imagines it's toxic. "One whiff and you're a goner" but Joyce originally wrote "One whiff and you're a gomer", a pun and also a slang term used at the time, like now. Many small typos and puns like this were fixed.
Check in your copy at the end of the Ithaca chapter (next to last, just before Molly's soliloquy) and see if it ends with... "Where?" or whether, just under the "Where?" there's a big black dot. The dot is intentional, mark of a scientific proof, like saying "QED". Joyce had a tussle of a time getting that dot added because they'd think it was a blotch and take it out.
The biggie however is the "great" puzzle of the novel. Stephen, in the Proteus (beach chapter 3) remembers asking of his dying mother (or trying to ask) "What is that word known to all men?" and later, in the Circe (brothel) scene, confronted by his mother's ghost, he asks again "What is that word known to all men?"
Neither time he receives a reply. But newly found and omitted by an editors error, is a passage of 3-4 lines in the Cylla (library) scene, when Stephen asks himself, "Do you know what you are talking about? Love, yes. Word known to all men" Love is the answer. Heck, John Lennon could have told you that.
And of course, the book is based on love, or the need for love, and Molly finally answers Yes, Yes I will. Yes. A reaffirmation of love.
Anyway, find yourselves a Gabler edition -- they're cheap, well made, large print, and this edition is the most complete and authentic available.