For my kids, going straight up to the fourth floor was the way to go. There are so many exhibits that are "representations" or "how it would have looked". The first floor is full of taxidermied animals, like you might see alive at a zoo. This was weird to me to see at a museum. Many of the exhibits were not lit well enough, even when there was information to read about. The gem exhibit was nice. Don't expect to be able to sit down to eat lunch or a snack as there is WAY too little room for very many people in the cafe areas. Also, the food is crazy expensive, even for NY attractions.
One nice thing is that you can enter straight from the subway.
We found this trip very enjoyable, using the Viator.com website made it easy and took the hassle out of it.
Wonderful museum. Directions to get tickets were not correct.