Building and organizing a basement on Long Island can be a challenging task if you do not follow a few simple rules. The depth of your basement mainly depends on how high the water table is. Also you might want to be out of the storm surge flood zone. The water table varies on Long Island. Basically the higher you are above sea level the safer you are from getting water. Although that is not guaranteed. Some areas on the north shore have a lot of clay in the soil which means heavy rains or streams can not drain away from your basement that could eventually end up in your basement.
Due to the way the glaciers formed Long Island the south shore ended up closer to sea level and the north shore ended up higher with hills and bluffs. You will find almost all of the storm flood zones and water table problems are on the south shore. The closer you get to the Great South Bay the more susceptible you are to potential storm flooding.
The ideal soil conditions for a Long Island home is of the sand/gravel mix variety. It allows for good drainage and good structural support. The soil on Long Island varies from town to town but this sand/gravel mix will allow water to drain away from your basement keeping it dry. There are spots on the south shore that are like this which allows for a dry basement. My friends basement on the south shore of Long Island in Bayshore stayed perfectly dry during hurricane Sandy. Not all basements on the south shore were flooded during hurricane Sandy. Check your location on flood zone maps for any confusion regarding if your home is in the flood zone.
There are water mediation techniques available to you if your heart is still set on finishing your basement even though you most likely have water/moisture issues in your basement. French drains or perimeter drains installed under the floor along the interior foundation walls is a typical remedy. Also the same can be done along the exterior of the home but at a much higher cost because of the necessary equipment and extra labor to dig out the yard. Also the possibility of reworking the landscaping. Since the foundation will be dug out at this point you may as well add a membrane or some other suggested water sealer to the outside of the foundation wall.