I just found a fascinating immigration article (April 1903) in the New York Times Archive titled Big Army of Immigrants: Nine Ships Bring 12,668 Foreigners from European Ports. The interesting parts of this article are the statistics. Of the total number of immigrants arriving, 8,561 were traveling in steerage; 4,500 of them were Italian with the rest being Germans, French, Swedes, Irish, English, Scots, Norwegians and Russians. The article says "...Swedes, who numbered about 1,000, were pronounced an unusually fine lot..." There is also an interesting comment that "there were no Jews among the arrivals." Sixty percent of the total were processed and sent to the railroads "for transportation to various parts of the country, principally the West, where they will work on farms." The article also talks about Ellis Island having to provide lunches for the train passengers that consisted of "8,000 pies, 5,000 pounds of bread, 5,000 pounds of bologna sausage, and 40 barrels of apples." In addition to the train passengers, they had to also feed a few thousand immigrants still on Ellis Island.
I need to spend more time looking at these old newspaper articles - they really give you a flavor of what the process was like. I think I'm going search and see if there are any good ones around the time my grandmother arrived (Oct 1913 - although she got off the ship in Philadelphia, her ship first visited New York harbor before heading south.)