All the people debunking "don't listen" are using anecdotal examples to miss the point: it's the odds. If you go Ivy, your odds of that fancy-pants job will improve. I recently finished my stint on my big-firm hiring committee, and saw this battle fought time and again. I'm all about small schools and grit, but that view loses out repeatedly to the view that pedigree matters. Obviously the Michigans/Virginias (state) will win out over the Cornells (Ivy), but again, you're using anecdote to argue against the underlying truth. Pedigree matters.
Having said that, for the OP, you go to the best state school in your state, or you find the private school that will throw money at your kid. We just went through this exact process, and my kid chose the high-ranking state school over the Ivy schools that granted admission; also in the mix were private schools offering essentially 100% scholarships. There was no comparison between getting out debt-free, after 80k total tuition, versus carrying debt after 70k per year. Granted, we're looking at grad school next, and that's where the kid will buff the resume with a higher-ranking school (to the extent there is one) in the chosen field.
But where "don't listen" misses the point is that mountains of people making big money at a hedge fund or fancy law firm are making less than lots (many/most?) quality solo and small-firm practitioners who went to a less-fancy school and therefore "lost out" on the big firm job. Because I have friends who went the "less prestigious" route, I know that I make roughly 50-60% less than they do, and I work 30-40% more, at the same seniority level. You tell me who is better off. Granted, we all started out at less prestigious schools, so it's unlikely (again, odds) that any of us will be President. But if you have any sense of the kid's life goals, you'll know whether this is an issue. Most everyone doesn't care.