Welcome to the site!
When you say you were able to get your shotgun permit over the summer, do you mean your shotgun license or are you talking about taking the shotgun hunter education course? There are specifically shotgun "permits" which are Zone and DMZ specific for the special permit shotgun season. Keep in mind that is different than your firearm license which allows you to hunt with the shotgun during 6-day firearm season (for deer), small game, etc. However there are A LOT of regulations here in NJ, so be sure to read the Hunting & Trapping Digest cover to cover!
If you have any questions along the way, post them up, lots of helpful members here will chime in and get you on the right track!