Congratulations on your new business!  When you are self-employed, the entire burden for paying employment taxes and prepaying estimated income tax liability is left to you.  Although estimated payments are not required, you should consider making estimated payments to avoid a large tax due when filing your taxes and also to avoid any underpayment tax penalty.  The amount you pay to independent contractors reduce your profit, which in turn reduces your taxable income.

Many newly self-employed people are surprised at their tax bills at the end of the year because they notice they're suddenly paying a lot more in tax as a self-employed person than as an employee. That's because they're carrying the full burden of paying for their Social Security and Medicare.

Here is a great resource for self employed taxes;

https://turbotax.intuit.com/tax-tips/self-employment-taxes/the-self-employment-tax/L8xXjolB4

When do you make the payments?  For estimated tax purposes, a year has four payment periods. Taxpayers must make a payment each quarter. For most people, the due date for the first quarterly payment is April 15. The next payments are due June 15 and Sept. 15, with the last quarter’s payment due on Jan. 15 of the following year.

The IRS has guidelines that will be helpful to your specific situation, including the 

https://www.irs.gov/newsroom/the-basics-of-estimated-taxes-for-individuals

I hope you find this helpful!