NeedSpace - what will be the purpose of your firearm? For sport? Hunting? Home defense? If for home defense, I would consider looking into handguns, since they are much more flexible and versitile for home defense. If you have a shotgun, it can be a bit difficult to set yourself up in a defensive position and get that thing pointed in the right diriection quickly. Get the right tool for the right job.
Your concerns about firearm safety with children is valid - but keep in mind - not matter what firearm you buy, you must be diligent with children around. I don't have children of my own, but all I can say is - it matters not what type of firearm you have -- you must keep firearms secure and away from children. An improperly secured shotgun can be just as deadly in a child's hands as a handgun. Bottom line: get the firearm that is best suited for your needs, knowing that you will apply the appropriate safety measures for it.
I went through the FPID / gun permit process last year -- from start to finish, it took a total of 9 months before I received my permit and FPID. BTW: By NJ state law, a municioality has 30 days to perform all the necessary background checks - they are not supposed to take any longer than that, but many do.
There are many gun laws in NJ that are designed to trip up law-abiding citizens and land them in jail. For example, if on the way to the range, you have a medical emergency like a heart attack, and you drive to the hospital, you can land in jail for 3.5 years with no eligibility for parole. We have this 'no deviation' rule where you can transport your unloaded and properly securty firearm to the range and back, but no where else. No stopping for food, no stopping for ammo, gas, whatever. I strongly suggest you purchase, read, and memorize this book:
If you are into podcasts, subscribe to the Gun For Hire podcast - lost of good insight there.
As far as ranges go in the North NJ area - there's the Woodland Park Range Indoor Range in Woodland Park, as well as Thunder Mountain up in Ringwood. If you are interested in going to the Woodland Park Range, ping me via PM and I can meet you there - I'm a member. They have many guns to rent - handguns, rifles, shotguns -- it is a good idea to try a few before you decide what to get. BTW: no FPID or any type of permit needed or required to shoot at the range there.
-Z-man.