I have seen both sides; I went to government school until part of the way through sixth grade, then was homeschooled until college. I can’t tell you strongly enough how much better homeschooling was in every fathomable way. 

Especially in the internet age, homeschooling can be done cheaply. Ask around; join some forums and groups. If your baby isn’t even here yet, you definitely have some time to research. 

Private schools may also have scholarships that can ease your financial burden. I have no direct experience with those, though.