I'm in Morris County too (North Jersey)
For you sir, the following
1) Post-Ban ARs are a-okay
2) Pistols legally acquired are a-okay
There is no madatory registration for bringing firearms into the state.
Get a Firearms ID Card. Go to your local PD and say you would like to get a Firearms ID Card. It is not necessary, but gives the police a feel good feeling if they pull you over, and you politely tell them you have arms in the trunk (also not necessary but courteous). Also, have proof (receipts, all forms you have, etc) in a safe place in case you have to prove you own anything. In almost any case, when in doubt, the police will assume you are guilty (relieving you of your arms) until you come to them with proof of legal ownership and that you are still elligable to own them (where the FID helps).
Stay safe in the Garden State,
p3
(mind you there is a list of banned weapons in case you have something else you were planning on bringing in. Also, besides the list, silencers are 100% not okay. =( ).