What are rules for filing

If you file joint return, on NJ return your wife is resident and will report her income. You are non-resident in NJ with no NJ income.

On NY return, you will report your income as resident and your wife is non-resident.
Your U.S. Tax Return: Working or Living in Two or More states

You should BOTH go to a local tax professional.

Whatever the fee will be, it will be worth it, because your joint return has so many pitfalls that the average lay person is bound to make a serious mistake.