Coming in late to this thread, but these are my comments as a teacher of high school seniors and the mom of two college students:
We started saving for our children's educations before they were conceived; it was important to us. Most of our friends lived in nicer houses, went on nicer vacations, and ate out more often -- but we valued knowing that we'd be able to write the checks for our kids' college educations, so we saved. Turns out, we over-saved. I have no regrets on that subject!
Our oldest will graduate in one more semester, and IF we'd paid "sticker price" for her education, it would've been just a hair over 50K. It's a state school, her first choice, and she has thrived from Day 1. You don't have to save a quarter of a million! However, we are in a cost of living area, which means that our salaries are low too, so 50K is more here than it would be in other parts of the country.
It's fine to put limits on how much you're willing/able to spend on college. With rare exceptions, your kids won't be better off in a private school or an out-of-state school, so don't splurge on big ticket schools unless you have a really solid reason for doing so.
Don't feel that you have to save the whole cost of tuition. You'll probably still be working and will be able to supplement your savings with current earnings. For example, if you expect your child's costs to be 15K per year, and you've saved 40K, you can probably swing the 5K out of current earnings -- that sounds a whole lot more do-able.
Too many people count on scholarships swooping in to save the day; for the vast majority of our students, this doesn't happen -- and if it does happen, it's more likely to be tuition-only than a full-ride. Yes, a decade ago, full-rides were more common, but today colleges have decided that it's better to give tuition-only to five students instead of a full-ride to one student. From a business point of view, it's a valid choice.
In all fairness, I should say that as many times as I've said, "SAVE! Don't assume your kids will get scholarships!", I'm pleased (and a little surprised) to say that BOTH of mine are currently in college ... on full scholarship. I paid a total of $330 for BOTH of them to attend school this fall semester, most of it going for my freshman's books. It does happen, but for BOTH kids to "win" is incredibly rare. I personally know only a handful of other people who can say this same thing. Scholarships aren't JUST about academics: The biggest scholarship winner is likely to be a well-rounded kid with good grades, leadership experience, financial need, who is entering a scholarship-heavy major.
People sometimes think that if they don't save, they'll "win" by being awarded financial aid. Yes, this is true: However, what you need to realize is that the aid these people are offered is NOT grants -- it's loans. Essentially, you can save now or make payments (with interest) later.
The private-school-gives-so-much-money-that-it-is-cheaper-than-state-schools thing is basically dead. I've been teaching seniors for more than two decades, and the last time I saw a student get a deal like this was the year my oldest graduated: that was 2012. It's an urban myth. Here's what's typical: The private school costs 35K/year and the state school costs 15K/year ... the private school offers you 10K/year and the state school offers you nothing -- so, yes, the private school offered you more, but that still leaves you with 25K, which is 10K more than the state school! If you think you'll get a great deal -- apply! try! But also apply to a school you can afford if nothing comes through for you.