There seems to be a good amount of interest in first-hand or contemporaneous accounts of immigration journeys, which certainly act as a counterweight to the family stories one hears.

For reasons that are unclear to me, my grandfather used to say his older brother Eli missed the boat from Liverpool to Philadelphia, because Eli ran after a man he thought was his Uncle Max at the dockside in Liverpool. Except - I found the ship passenger list for the trip from Liverpool, and little Eli was on the boat, along with the rest of the family. I don't know how these stories get started.

For some other first-hand accounts - 

A young Jewish woman named Mary Antin, who immigrated with her family from Polotzk, Belarus, to Boston in 1893, wrote a memoir about their lives there and in the US. The entire book has been digitized, and it is the chapter called 'Exodus' that describes their journey:
https://digital.library.upenn.edu/women/antin/land/land.html

Not for the faint of heart - Here is a 1909 report by the US Immigration Commission on steerage conditions on immigrant ships. The best that can be said - at least on the bigger ships, there was kosher food:
https://babel.hathitrust.org/cgi/pt?id=chi.083689176&view=1up&seq=1

And on the legal status and conditions for Jews in the Russian Empire, written in 1906 by a US foreign service office from the embassy in St. Petersburg:
https://history.state.gov/historicaldocuments/frus1906p2/d409
--
Michele Lock

Lak/Lok/Liak/Lock and Kalon/Kolon in Zagare/Joniskis/Gruzdziai, Lithuania
Lak/Lok/Liak/Lock in Plunge/Telsiai in Lithuania
Trisinsky/Trushinsky/Sturisky and Leybman in Dotnuva, Lithuania
Olitsky in Alytus, Suwalki, Poland/Lithuania
Gutman/Goodman in Czestochowa, Poland
Lavine/Lev/Lew in Trenton, New Jersey and Lida/Vilna gub., Belarus