What is the best way to research your ancestors who came into the US through Ellis Island?

My great grandparents, my grandfather and all but one of his brothers and all of his sisters immigrated to the US in the late 1800's from Hanover, Germany. The eldest son remained in Germany because the eldest son by tradition would inherit the family farm. When they all came through Ellis Island, their name was changed from Roemke to Romke by one immigration official. Regrettably, I need not ask my grandfather any questions about his immigration. All he told us was that we should get all of the education that we could, because no one could take that away from us. In Germany, the government took much from its citizens. Life in the US was very good for my grandfather. He and my grandmother had two children, bought a farm and made a very good life for themselves, their children and consequently for my sister and myself. Now I would like to learn more of what happened when they entered this country and how they came to make their home and success in the midwest.