You can own an AR platform rifle in NJ provided it is a NJ compliant model. To be such, as a magazine fed, pistol gripped rifle, it must not have ANY of the following; bayonet lug. retractable/adjustable butt stock and a flash hider/muzzle brake. Bushmaster, from whom I chose my AR, make the following model which is NJ compliant.
A quick call to the NJ State Police firearms information hotline will get you a friendly trooper who will explain it all to you. Since the maximum allowable rounds for we NJ residents is 15 rounds, you can only get ten round mags or pay through the nose for a 20 or 30 pinned to fifteen.