I have been trying to plan out some financial decisions for next year with a new job and a general idea of how much I will be paid, and have been trying to understand if claiming 1 or 0 in the future will be worth it and how much of a difference it would make? Ideally understanding how to bring my net taxes to near 0 while taking home as much as possible per month.
The new W-4 form doesn't use allowances anymore, so you no longer claim 0 or 1 or any other number of allowances. The new form works differently. Use the IRS Tax Withholding Estimator at the link that Critter-3 posted above to figure out what to put on your W-4 form. It will show you how to adjust your withholding to get the approximate refund amount that you want.
The W-4 form which you fill out for your employer is designed to withhold the proper amount of tax.
The new W-4 form doesn't use allowances anymore, so you no longer claim 0 or 1 or any other number of allowances. The new form works differently. Use the IRS Tax Withholding Estimator at the link that Critter-3 posted above to figure out what to put on your W-4 form. It will show you how to adjust your withholding to get the approximate refund amount that you want.