As a collector of first editions, there is some general, conventional wisdom worth sharing here - you are welcome to disagree with it completely.
For the 1800’s, the G.A.N. candidates most often cited - and which are considered the most collectible, to the extent that matters - are:
Adventures of Huckleberry Finn by Twain
Moby Dick, or The Whale by Melville
The Scarlet Letter by Hawthorne
Red Badget of Courage by Crane
Others get mentioned - e.g., Little Women and a few others - but these are really the Big Four. Of these 4, Huck and Moby Dick are generally considered the standouts. And, typically, you can think of them differently - Huck is the more accessible Voice of the Common Man type of book and Moby Dick is the academically rich, critically respected book - obviously Huck is critically appreciated, too - but Huck’s popularity started from the people and reached the critics, whereas MD sold poorly and was basically forgotten until it was re-discoverd by academics and re-introduced to the public about 50 years later…
My preference is Huck.
As for the first half of the 20th century - the books commonly held to be the best are:
The Great Gatsby by Fitzgerald
A Farewell to Arms by Hemingway (The Sun Also Rises made a big splash, but Farewell is considered his best book)
Sound and the Fury by Faulkner (some prefere Light in August or As I Lay Dying)
The Grapes of Wrath by Steinbeck
Arrowsmith by Sinclair Lewis (some prefer Babbitt, with his breakthrough book, Main Street, not as well respected. Lewis is making a bit of a comeback as the first American to have won the Nobel…)
Of these, Gatsby is pretty much considered the G.A.N. because of the beauty of the prose and more importantly the subject matter of class distinction and trying to live the American Dream of re-inventing yourself to move between classes, the way Gatsby tried and succeeded in doing only to fail in the end.
As for the 2nd half of the 20th century, the generally held best are:
On the Road by Kerouac
Catcher in the Rye by Salinger
To Kill a Mockingbird by Lee
Catch-22 by Heller
Gravity’s Rainbow by Pynchon
Of these, Catcher and Mockingbird are considered to be the standouts, simply because Pynchon’s book is critically hailed, but almost no one has read it, whereas Cather and Mockingbird have such huge, enduring crossover appeal that they simply leave Pynchon in the dust. If a Great American Novel is only read by a cult few and academics in the forest, will it make a sound?
Of Catcher and Mockingbird, while Catcher captures the voice of the newly-recognized and disillusioned teenager, Mockingbird tends to win out because it centers on American themes of racism and shows America, in the form of Scout, transcending its racist past, with Atticus in the form of a virtuous founding father.
I would add Tim O’Brien’s The Things they Carried to the 2nd Half of the 20th Century list, and Richard Wright’s Native Son to the 1st half list (and others have been adding Zora Neale Hurston’s Their Eyes Were Watching God, too), but they are as widely recognized as of right now…