Tax Year Prior to 2020: I live in Arizona and am self-employed. I would like to find out how much of my income I should put aside. I am a cash-basis tax payer.

It depends on how much you earn and your expenses.  For federal taxes, there are two amounts that need to be added together for your estimated tax payments.  The self-employment tax rate of 15.3% plus your ordinary income tax rate (which depends on your taxable income and filing status).  The following article has easy to read tables for this amount http://taxfoundation.org/article/2017-tax-brackets 

How you figure out your estimated amount is to take your gross self-employment income minus expenses to get your "net" taxable self-employment income.  Then, multiply that by the 15.3% self-employment tax rate.  Then, look up the rate on the charts for your annual total taxable income (in the link above)  and multiple that by the percentage for your total income you expect for the entire year. Add those to tax amounts together.

For Arizona, this following link has the tax brackets for 2017,  https://www.tax-brackets.org/arizonataxtable