your walther p99... why you brign it with you. If you are really felling paranoid get an FID card. Handgun permits in NJ are for purchasing, which you have already taken care of.
heck even if the smart gun law was in effect, you'd still be able to bring it as the law is on the transfer of firearms in NJ. Which you didn't do.
If you want a crash course on the NJ firearms laws translated into english, go here and pick up a copy. It even covers all the nitty gritty on moving here.
http://www.evannappen.com/nappenii/
You won't be getting a CCW though, but I'm guessing you already knew that.
The only caveate with the p99 is that if you picked up any 16 round magazines, you need to block them to 15 rounds. Not having seen a p99 16 round mag, I have no idea how hard or easy this is.
however, like others, I suggest you do what you have to to stay away. If you drive a car, you will get whacked with an insane insurance charge as a new resident beyond the run of the mill insanity. IF you can find an insurer willing to write youa policy. Most of the doctors won't take new patients, and if they do, they don't take an awful lot of insurance. Homeowners insurance policies are getting ahrder and harder to get. REal-estate prices are insane. A 9 mile commute can take you 40 minutes. We swap out congressional candidates at the last minute, as well as try to appoint mafia figures head of the state police.. multiple times. In the summer traffic gets worse because of the beaches. in the winter The traffic gets worse because of the malls and the fact NYC has 8% sales tax and we don't. Cigarettes cost about $6 a pack and they want to tack another $1.30 tax on them.
And frankly it has made us, on average, a pretty surly bunch.
oh yeah, did I mention our state congress is insane enough to want to pass a "smart cigarette" bill. Looks exactly like the smart gun bill except it mandates the development of fire retardant cigarettes, cops aren't exempt, and the penalty for transferring a normal cigarette is $11,000.