I am from Pa. and hunt both states. Pa. is relatively free and does not have rules about bringing guns here (assuming you are not a felon), but if you intend to hunt you have to follow Pa. Game Commission regs re caliber/gauge, ammo type, etc. As for shooting, the only limitations are those imposed by the ranges themselves.
NJ is more like California with respect to guns. Nonetheless, there are gun clubs there and we hunt, though not with centerfire rifles.
Since gunwise, it is a semi-police state, I would double check all information I got from the Internet.