There is no set answer, because the amount you should pay in estimated taxes (technically, this is not withholding) depends on a variety of factors, none of which we know because we can't see your tax return.
Know this:
if you are self-employed, then on the net profit from your Schedule C, you will owe federal income tax based on your tax bracket, and you will also owe 15.3% on 92.35% of your Schedule C net income in self-employment taxes.
So let's say that you are in the 12% tax bracket ($9,701 to $39,475 if you are filing as Single). You won't owe any more than 12% of your net income in federal income tax (and will probably be less). So the most you would owe on your net income is 27.3%, and will probably be less.
Of course, we do not have any idea what your income will be nor your expenses, so you have to work these things out for yourself.
Likewise, without knowing your your net income, we can't know for sure your Missouri tax burden, but the highest tax rate (and the bracket is pretty low) is 5.4%, so your state tax should not be larger than that.
I don't know where you work, but do you have a board of elders or a parish council on which serves a tax professional or an accountant? I am talking about people who would know your pay so you would feel free to discuss tax matters with him/her.
Ask this person for a bit of pro bono work to help you estimate reasonable amounts to pay in estimated taxes. With a little work, you should be able to estimate a percentage amount of your gross pay for both federal and state, which will be the easiest way to make it work.
After the first year, you should have a good idea of what you actually owe, and you can readjust your estimated taxes then.
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