What are three significant things the four men brought with them?
I cannot see that the four men in the story brought anything with them to the setting inside the cave. Three of the men are visitors and evidently brought nothing because they have nothing to bring. The host, Doctor Jenkins, who may be a former medical doctor or a professor, has three very important possessions which he keeps hidden in his cave-home. They are a tiny collection of books, a collection of old phonograph records, and a portable phonograph which has to be wound up. The fact that the phonograph is an old portable is important because there is no electricity and only a wind-up phonograph would be of any use in playing the records. Jenkins has been using thorns in place of phonograph needles because he has only three steel needles left.
"Shakespeare, the Bible, Moby Dick, the Divine Comedy," one of them said softly. "You might have done worse, much worse."
The Shakespeare is most likely one of those big volumes containing the complete works. The novel Moby Dick was written by Herman Melville. The Divine Comedy is a long poem written in Italian by Dante Alighieri between c. 1308 and his death in 1321, but no doubt the edition owned by Doctor Jenkins is an English translation.
He had a dozen records with luxuriant gold and red seals.
Apparently they are all classical music. Only two titles are named. One is George Gershwin's "New York." The other is a nocturne by Claude Debussy.
These are by far the most significant things in the story--the collection of books, the collection of records, and the precious portable phonograph. The reading from Moby Dick and the playing of the Debussy nocturne seem to cause the visitors as much pain as pleasure, because these treasures of a lost civilization remind them of everything else, including New York City itself, that is gone forever.
There is no greater pain
than to remember, in our present grief,
Francesca da Rimini, in Dante's Inferno