packing.org is good, also look at
www.evannappen.com
He wrote the authoratative book on NJ gun law.
If you are moving in with your guns you should be ok transporting them locked, ammo separate as in any other state (keep in mind that as you travel up, in some states like Maryland, a loaded magazine, even separate from the gun = a loaded gun.)
You don't have to register them.
Some caveats, like anything with more than a 15 round capacity is illegal based on our own homegrown state AWB. No grandfathering. Hollow points are also illegal except under certain circumstances etc.
(Get the book!)
Also, the process going forward for you in NJ is you need to apply for a FID (firearms ID card) and depending on where you are that can take upwards of 6 months (liberal democratic counties closer to NYC = 6 months as you get out in the mountains, more conservative less hassle with guns, less permit time.)
(This is in spite of the fact that there are laws saying it can take no longer than 60 days I believe.)
The FID card entitles you to buy all the long guns and ammo you want. Handgun caliber ammo must be logged in a book but it is legal to buy over internet or mail order (no log there.)
Handguns require a pistol purchase permit. You are limited to one purchase per month. Permits are good for 90 days. In my town, we get them in two weeks (sussex county). Elsewhere it can take months and the local PD's can practice their own version of gun control by repeatedly losing your application and just giving you the run around. Keep your receipts and keep good documentation in general. Be persistent, they can't legally deny you.
Lots more info, as you have more questions, fire away.
Not a gun freindly state, if that's an important part of your lifestyle, consider moving to nearby Pennslyvania. Lot depends on where you will be working as commuting from PA to areas where most of the decent jobs are is not practical
Good Luck!