Rank of the college matters in my opinion. It's unfortunate but it does create opportunities. High-ranked public universities are often really great, but usually comparable in total cost to private ones (with savings for being in-state in some cases).

But yes if you only gain admission to the long tail of private colleges, then you would almost certainly be wiser to go to a low-cost public school.

I wouldn't want my kids to consider community college unless they had to. By definition, I'd like them to have the same academic opportunities I had, if possible.