IfI am working 40 hours a week at this lil store and they are filing a 1099 tax form.....how much should I take out a week towards my taxes?

You are a W-2 employee. If they are saying you have to pay your own taxes and will be sending you a 1099, they are not only breaking the law, they are cheating you out of the reporting of your income for a future Social Security retirement benefit.

You still owe your share of Social Security and Medicare tax, but they are trying to stick you with the share that they are supposed to pay. You need to contact your state's Labor department to get this to stop.

Nothing because you are an employee and should have taxes withheld. You should contact your state unemployment tax agency and tell them and they will set your employer straight.

QUIT!!!!
It's illegal for them to pay you as an independent contractor.

If they are cheating you for a few dollars, how else do they break the law?

your self employment tax will be $45.29 for each $320 check you get
the point is if you anticipate your combined taxes to be $1K or more you need to predeposit on for 1040ES and the last voucher for 2017 will be due Jan 15, 2018

That's between $16,000 and $17,000 a year. Figure about $600 for federal "income" tax each year, so $11-12 a week for that, and about $45 per week for federal "self-employment tax". That's a total of $56-57 a week, plus whatever the state tax is in your state. Go with $65 a week, that should be enough.

About 35%, they are screwing you.

Depends on a lot of things.- where you live, how much you make, your filing status, spouse's income if you're married, dependents. For most people, 25-35%. A 1099 is almost surely illegal for them to do, but that's a separate question.

Complain to the IRS they are cheating the tax system. Independent contractors need to be paid 2-3 times as much as employees and need to be independent. They can't tell you what hours to work or some other things and not have you be an employee. If you are self employed they won't cover you with unemployment or workers comp or pay your SS so you pay double. You need to pay estimated taxes quarterly not save the tax money yourself. Pay in 30-35% of your pay for self employment and income taxes.
Quit the self employment isn't worth it for what they are paying and illegal for them to try it.

Just ask payroll what the percentage is. You can do it monthly because if you wait every 3 months, the fees will be higher

They should not be filing a 1099. That's for independent contractors. You are an employee. They should be withholding taxes from your pay and filing a W2.

That's fraud, and do not go along with it. You are an EMPLOYEE, not an independent contractor since you work in the store. Demand they pay you properly as an employee, including their employer-paid contribution to Social Security & Medicare as required by law, or quit & report them to IRS Fraud Hotline. Do NOT become complicit in tax fraud! Or YOU are in trouble as well as the employer.

Sounds like they are committing tax fraud.