Wayne,

No permit to buy rifle or shotgun ammo. Pistol ammo you need to electronic certify that the ammo is for a handgun and you are a permit holder. Not in every store though, seems like Walmart, Dicks, Field and Stream, etc.
One time I purchased 22LR ammo at a Gander Mountain, I was asked if it was for a rifle or handgun.
I believe in NJ you need a firearms permit to buy ammo. Not sure if that applies to all ammo.