It is best to buy tickets online and in advance when visiting the Intrepid Museum. It makes getting through the entrance faster.
It can be very hot on top of the aircraft carrier, so hats are a good idea. On the other end of the spectrum, the submarine museum is a tour of an actual submarine. The entire tour takes place in a tight enclosed space.
There is a lot of walking at the Intrepid Museum, so the best time of day would be when you and your family have the most energy.
The museum wasn't too crowded in August, arguably at the height of tourist season in New York, so it seems like anytime would be good to visit.
There is enough to do and see at the museum, you don't need to spend the extra money on additional activities such as the G-force simulator or the 4D experience.