This information is available free of charge on stevemorse.org and a free subscription with ellisisland.org will give you access to 'The List or Manifest of Alien Passengers for the U. S. Immigration Officer at Port of Arrival'
Information may include
Port of Departure
Date of Arrival in the U. S.
Race or People
Ticket to final destination
By whom paid
Whether in the States before
Name & Address of relative in the U.S.
The Name and Address of the relative in the U. S. will either open a whole new line of research or it may confirm that you have found YOUR family member.
Good luck and let us know if you strike gold!