NC withholding form to use NC-4EX, NC-4 or Non-resident alien?

Form NC-4EZ would be fine for someone with a very basic state tax scenario, without numerous adjustments, itemized deductions or state tax credits. 

According to NC-4 Instructions, available at Withholding Tax Forms and Instructions,  you would "use Form NC-4EZ if you plan to claim either the N.C. Standard Deduction or the N.C. Child Deduction Amount (but no other N.C. deductions), and you do not plan to claim any N.C. tax credits."

Form NC-4 would be useful for more complicated scenarios. The NC-4 instructions suggest using it to "help you determine your withholding allowances based on federal and State adjustments to gross income including the N.C. Child Deduction Amount, N.C. itemized deductions, and N.C. tax credits." 

You don't indicate that you're a non-resident alien -- an alien (not a U.S. citizen) who hasn't passed a green card test or substantial presence test, so Form NC-4 NRA wouldn't seem to apply.