Okay - let's set all the doom and gloom aside for a moment.
By law, you don't have to do anything to bring your firearms to NJ with you. You must transport them unloaded, locked in the trunk or in a locked case, with any ammunition stored separately from the firearm(s). Once you enter NJ, you must travel directly to your place of residence.
As long as the firearms are NJ-legal (no magazines over 15 rounds capacity, no "assault firearms"), you can possess them in your home without any licenses, permits, or other paperwork. Registration of firearms in NJ is voluntary, and, IMO, not recommended.
As for "assualt firearms", that refers to semi-automatic rifles and shotguns with certain characteristics and features. Since you're only talking about handguns, we won't go in to those details.
The particular statutes you're interested in (and which I encourage you to read) are 2C:39-5, which says that possession of a handgun without a permit to carry is illegal, and 2C:39-6e, which says that the previous statute doesn't apply to someone possessing firearms in their home, or transporting them from one place of residence to another while moving. 2C:39-6g describes the storage requirements for transportation, as described above.
All of these statutes can be referenced at the
New Jersey Legislature web site. Find the 'Statutes' link on the left.