NEW YORK — As Andrew Hacker and I began researching our book, “Higher Education?” we were struck by how few questions parents raised when considering the quarter-of-a-million-dollar investment that four years at a private college or university could cost them.

This was, probably, the second-most-expensive purchase they’d make in their lifetimes; yet many decisions seemed to be based on the familiarity of the brand name or the attractiveness of a campus.

After three years of researching our book, these are the questions we’d ask, if we had a high-school student at home: Does the college make undergraduate teaching its first priority?

Schools like Harvard and Stanford have almost twice as many graduate students as they do undergraduates, and it’s the graduate students that command most of the professor’s time and attention.

Is the college overrun by administrators?

Yale has 1,050 full-time faculty members and an additional 7,013 people in nonacademic jobs. So ask: Is it primarily a college, or is it a multiversity festooned with extraneous functions?

Will professors actually be there?

During a recent year at Williams College, a third of its professors were away on leave. Your daughter may find that her senior thesis supervisor is on sabbatical in Bologna.

What’s the president’s salary?

Increasingly, it’s nearing or more than $1 million. This is a good index of whether a school has chosen a corporate model. Decide whether the person at the top looks and sounds like an educator.

Who teaches the freshman class?

It may be a star professor (but the odds are against it). But at most name universities your son will be in the 26th row, with a fledging graduate student handling the discussion section.

Can you walk in for water polo?

At many colleges, athletes are recruited beforehand by coaches, so others find the rosters are filled. At the University of Illinois, only 2 percent of its undergraduates are on teams. The rest have to settle for being spectators.

How much emphasis is on athletics?

Small Birmingham–Southern College has a 90-man football squad, supervised by eight paid coaches, while its history department makes do with five professors. Its softball team plays 34 games in a 10-week season, half of them away, leading to missed classes.

Does the financial-aid office level with you?

Today, what’s called aid is usually a discount on the sticker price or, more likely, a loan. Does the college spell out what the actual interest charges will be, what happens if payments are deferred, and how old your children will be when their debts are finally paid off?

Does it resemble a resort?

Five-story climbing walls, gigantic Jacuzzis, food-court chefs specializing in chicken Dijon  — all come under what used to be called “room and board.” It also diverts funds, and helps explain why so many of your child’s classes will be taught by low-cost adjuncts and assistants.

Does prestige pay off?

Some parents (even if not you) want their offspring to be successes in life. Hence, they aspire to a college with name recognition. But ask for evidence: Do Dartmouth and Duke degrees really loft you to the top? In our book, we looked at the long-term achievements of one Princeton class. Considering the huge advantage these Ivy Leaguers had at the starting gate, their attainments, for the most part, were not all that remarkable.

In fact, you can get a fine education at a public university; in fact, even better than at many elite schools. Arizona State University, for example, has excellent “honors colleges” on its mega-campus, with small seminars and readily available professors.

But you have to look for such options. Otherwise, you will join 623 fellow freshmen in Biology 101 at Ohio State, or 578 sophomores in Economics 201 at Michigan State, where your exams will be graded by computers and you will squint at your professor from the 29th row.

Nor are public universities as open as they once were. At the University of Colorado, fully a third of its students come from out of state, and are willing to pay $29,493 for tuition, over three times the in-state tab. At the University of Virginia, preference is given to out-of-staters who pay $32,902, so many local students must settle for lower-profile branches.

Even so, our public colleges still make a degree possible at a relatively modest cost. You can start a liberal-arts program at Mount Hood Community College (two years’ tuition: $7,688) and then transfer to non-mega Western Oregon University (two years including room and board: $31,872). Your grand total for a degree will be less than two semesters’ tuition at many private schools.

After so many years of researching this American Way of Higher Education, we’ve come to believe that when parents are selecting a college for Jennifer or Jason, their primary target should be a school that permits their child to graduate debt-free. That means thinking creatively and forgoing dreams of luxury or prestige.

Unless the family is wealthy or the youngster can land a full-ticket scholarship that genuinely is that, the elite private institutions are probably best avoided.

Instead, parents might consider the honors college at their in-state public university, or the first two years at a community college, many of which are staffed by dedicated professors who like teaching.

Families might also consider a commuter school —$40,000 to $100,000 can be saved by taking the subway.

• Clauia Dreifus & Andrew Hacker