Whether you choose "0" or "1" on your W-4 will have a significant impact on the amount of your federal income tax return. Claiming "0" essentially means you are planning for no standard deduction, so you will have more in taxes withheld from your paycheck.
Claiming "0" may be the better option if you are satisfied with the amount of your net pay and are not concerned with the additional amount being taken off your paycheck. You are also more likely to receive a larger tax return. Claiming "1" is the better choice if you need a larger amount of take-home pay.
If you wish to adjust the amount of your withholding, you should contact your employer. The company can supply you with a new W-4 to make the change.