New Jersey only allows certain deductions from income and does not have a true itemized deduction.  They do allow a deduction for property taxes, but not for mortgage interest.

In regards to New York, you can take the standard deduction even if you itemize on your Federal return.

You would use whichever one is more beneficial.  If you aren't sure, I would not say that you plan to itemize.  This will prevent them from not withholding enough taxes.