Just been to NY in march. If you want to see the inside of Statue of Liberty, book your ticket well ahead.
http://secure3.gatewayticketing.com/statue...nelDetailID=224

Select the ticket with monument visit pass, otherwise, you wouldn't be able to have a close up with the statue.

I travelled through Battery Park. You can bypass the long queue to purchase ticket and pick up your booked ticket at the counter. The security is crazy before you board the boat, just like you pass through security at the airport.

To go in to the Monument, you need to store all your belongings in locker, of course, you need to paid. Only cameras is allowed in the monument. You need to pass through another security check for the Monument. You can go to the base of the Statue of liberty, but not climbing her. Without monument pass, you won't be able to see the back of her. Strongly suggest you book your ticket before you go.

In addition, plan plenty of time to visit Ellis Island, the last boat from Statue of Liberty is 3.30pm.