AFAIK:
There is no need to involve an FFL regarding your own firearms that you personally bring into the state when moving in.
DO NOT bring in anything NJ classifies as an "assault weapon":
http://lis.njleg.state.nj.us/cgi-bin/om_isapi.dll?clientID=183272087&Depth=2&TD=WRAP&advquery=assault%20weapon&depth=4&expandheadings=on&headingswithhits=on&hitsperheading=on&infobase=statutes.nfo&rank=&record={1770}&softpage=Doc_Frame_PG42&wordsaroundhits=2&x=0&y=0&zz=
Summary: 19 named armaments, or any semi > 2 evil features.
Incidentally, pistol grip shotguns are OK, as long as they aren't semiautomatics. I've seen pump shotguns for sale in jersey complete with ALL the evil features: folding stocks, pistol grips, barrel shrouds, etc
Hi cap mags: nothing over 15 rounds, temporarily or permanently blocked mags are OK.
FID: get one, ASAP. Keep your guns in your home until you've got that all squared away, and spin yourself up on the laws.
My advice: **** with respect to exactly whatcha got. Registration of imported arms is entirely voluntary, and not to your benefit.
Disclaimer: I am not a lawyer, I am an informed layman, and former Jersey guy. Evan Nappen (
http://www.evannappen.com) is a lawyer, and a damned good one if you've got serious questions.