Based on things on here (so take it with a grain of salt), DC nannies typically need to be paid on the books because many employers have security clearances.
It might help if there are specific questions, and then DC nannies/NYC nannies can chime in.
Benefits:
health care contribution?
dental insurance?
paid federal holidays?
paid vacation time?
paid sick days?
gas mileage reimbursement?
metro card reimbursement?
Misc:
paid on the books or under the table?
hours worked
hourly pay