As a parent who has two older sons who are and have went to college my experience is that the poorer you seem on paper (your taxable income) the better your results for scholarships.
My older son received the maximum scholarship from a private university as well as grants that totaled about $35,000/ yr for a $40,000 / yr school. He took $5000.00 / yr in student loans to cover the rest. Although he is now in the military that will pay off all his loans. Plus he should be able to get his RN license by the time his enlistment is up.
My next older son who is in his second year at a D1 university received a fellows scholarship that paid everything (tuition, room and board, books, supplies) plus gave him money for a laptop.
My advice would be not to save one dime for your child for college. This is easy for me because I have a wife who stays home (even though she is a degreed electrical engineer) and homeschools my younger kids.
Make sure your son studies for the ACT the summer after his sophomore year and try to score a 27 or better. Also have your son take as many dual credit courses (classes that will count toward college) as these are cheaper while in high school. Both my sons ended up with about 24 hrs of dual credit courses before starting college.
There are some D2 schools in our area that will give a full ride to any student scoring a 27 or better on their ACT.
Also the military can be an option. It will pay for your tuition (GI Bill or Montgomery Bill).
I have a 13 yr old son who has demonstrated a knack for baseball and football. I will plan for him to get a full ride on academic but won't look away from a potential athletic scholarship. :O)
BTW, I don't think the education of the parents affect scholarships because both my wife and I are degreed engineers.