I live in New York City and have a handgun license (premise only). I also know someone that has a carry license. I own 5 handguns.
New York is a “May Issue†State when it comes to handgun licensing. Licensing occurs at the county level. Some counties are very pro-rkba and give out carry licenses. Other counties are very anti-gun and give people a hard time over premise licenses. In New York City, the Police Commissioner is the licensing authority. New York City leans to the anti side. However, it is fairly easy to qualify for a license. The actual process of applying for and receiving the license is far worse. Lots of hours wasted.
After you apply for a license, your application is assigned to an investigating officer. That officer will make a recommendation as to whether you should be granted a license. The officer can recommend against granting a license for any reason whatsoever. For example, if the officer decides that your residence isn’t secure enough, you won’t get a license.
There appears to be some confusion over “premise†and “target†licenses. There is no target license anymore. There are only “premise†and “carry†licenses. The “target†license was an invention of New York City, which was ruled to hold no weight because the licensing laws are state laws and New York City cannot usurp them. Hence, the appeals court viewed New York City’s special target license as a plain ol’ premise license. NYC now issues standard premise licenses.
The NYC premise license lists the premise in which you are allowed to possess guns, and the guns you may possess. The license also allows you to go directly to and from an “authorized location.†All NYC gun ranges are authorized locations, but it is unclear as to whether ranges outside of NYC are included. The police claim to have a list, but no one seems to know where it is. Personally, my experience is that you can go to any range outside NYC with no questions asked.
You can only get a carry license if you have cause. In some counties, protecting yourself is cause enough. In NYC, “cause†is the protection of money, or as part of a profession, such as a security guard. The carry license will generally restrict carry to working hours, or to times when you’re making deposits. It is near impossible to get a totally unrestricted carry license. Recently, many licenses of the “rich and famous†were pulled in an investigation. I think several thousand licenses were pulled for one reason or another.
New York State also registers handguns. That means that the state must know about every handgun you possess. Your handgun license will list every handgun you own, along with its serial number. My license has room for eight handguns. I have five. If you will be keeping more than 4 guns, you must have a safe. When I put in my purchase request for my fifth gun, I also had to submit two pictures of my safe (opened and closed) and the receipt for it. Only then would they approve the purchase request. You must always get approve before acquiring or disposing of a handgun. If the city doesn’t like the gun you want to get, they won’t approve it. For example, good luck getting a pocket pistol. I do not believe there is any limit on the number of handguns you can possess.
New York State has implemented its own “assault weapons†ban that mirrors the federal ban, except that it doesn’t expire. So when the federal ban expires in September, New Yorkers still will not be able to buy new hi-cap mags. In addition, New York City has a 17 round limit on mags, regardless of when they were made. Also, a mag cannot extend beyond the bottom of the grip, so things like +2 extensions are not allowed. Also, you can only possess ammo for the guns you own. The calibers are listed on the handgun license. Having barrels or conversions for other calibers for one gun is a no-no. At least buying ammo is no problem. I can order 10,000 rounds from AmmoMan and have UPS deliver it.
Rifles are slightly different. New York State doesn’t have any rifle or shotgun registration or licensing. New York City, however, has implemented its own rifle and shotgun permit. This is a completely separate from handgun licensing. One really annoying requirement is that rifle magazines cannot hold more than 5 rounds. So you can’t even keep a Ruger 10/22 without a modified mag. It’s really ridiculous. I don’t have a rifle, so I don’t know much more about it.
. I don't have any 1st or 2nd hand experience with NJ so I can't help you there. I know you don't want to hear it but you really are better off not moving to CA, NY or NJ, trust me. There are jobs out there you just have to find them. 
