You don't need money in the bank to move out, besides first and last months rent (usually) and a security deposit. How much will depend on where you move to.
Obviously, you need an income to pay for expenses. Food, gas, insurance, rent, utilities, etc.
Ideally, you would save as much as you can. It sounds like your parents are supportive. Why not try to live at home and work for a few years, before looking at moving out? Rent is a waste of money, and you could always pay your parents rent. If they don't want the money, have them save it for moving expenses, or a downpayment on a house in the future.