I am looking at excepting a position in IN. 28,000 year salary 1099. I am single with 2 children. What % do I hold back each check? I also travel at work so will keep track of mileage.

As a contractor, you should DEFINITELY keep track of mileage and every other expense you incur, because it is more than likely deductible in one forms or another.

As for how much to set aside: if the $28K is your ONLY income source for 2018, you WILL qualify for both the Earned Income Credit for a significant amount ($5,000+) PLUS an additional $4,000 for the Child Tax Credit ($2,000 per child, assuming the children are both YOUNGER that 16 years of age).

Given these facts, you need to put NOTHING aside. You likely will owe NO federal income tax, and the MAX self-employment tax will be at most $4,000, and the Child Tax Credit will pay that, so you should be okay setting NOTHING aside. The only tax you may owe may be Indiana state income tax, but that will not be that much.