You'll have to bond with your prospective father-in-law at a PA gun show CAUSE THERE AIN'T NONE IN JERSEY! Valley Forge just happened a couple of weeks ago, but there's one coming up at the Armory in Northeast Philly soon. Not sure of the exact dates.
As a NJ resident in want of a handgun, he needs to go to his local police dept and apply for a Pistol Purchase Permit. One permit per gun, apply for up to five (I think) at the same time. Time frame, anywhere from 30 days till the cows come home, depending on his local PD, his references, and the phase of the 3rd moon of Saturn (j/k about Saturn, but it sure seems that way sometimes)
If he wants to buy a rifle or shotgun, he needs to apply (same place, same paperwork, same shit) for a Firearms ID Card.
As far as NJ gun laws go, you can check out
this reference page on the NJ Hometown site.
And good luck with your Jersey girl, Mickey!