Well it actually depends on how much time you have and for how long you are in New york. If you are in states for shorter time then probably you would take a ferry from battery park.
Going from battery park you may have to be in long queues for tickets then ferry and same when you take the ferry back from Ellis island and statue of liberty.
But if you are around new york for a longer time and you are traveling with kids then the best way is to rent a car and go to liberty state park in Jersey City. And if you are coming from Connecticut then I would suggest that you take Tappan Zee bridge and Garden state parkway. From Stamford, CT we found this route most convenient and traffic free.
From the Jersey side the queues are much much shorter, no waiting. Would strongly recommend especially if you are traveling with kids. We felt so relieved when we went there last weekend with nine month old baby, it would have been so hard to stand in long queues. Also the time that you save from standing in queues you can enjoy more on island.
The ferry from Jersey first take you to Ellis island and then to statue of liberty. Ellis island you will like if you love to learn history. You will enjoy more time at Statue of liberty, very good views of New York, if you can take a sheet would be good to sit on grass and feel the breeze coming from shore.
Have fun !!