WASHINGTON — American students are becoming more careful shoppers when it comes to choosing--and paying for--their college educations.

After a decade of soaring tuition costs, counselors say that students and parents are approaching the entire college-selection process with a far sterner eye on finances. More students are considering state universities and are applying for merit-based scholarships.

"We are seeing a trend of staying in-state and going to state institutions--especially those families who can't qualify for a full financial-aid package," says Regina Manley, a coordinator of activities for college-bound students in the Chicago public schools.

Frank Burtnett, the executive director of the National Assn. of College Admission Counselors, agrees. "Spiraling college costs have reached a saturation point in the eyes of many people," he says.

The financing problem intensified during the 1980s, when college administrators found themselves facing a shrinking market as a result of the birth dearth of the late 1960s and early 1970s--and a potentially sharp decline in revenues, to boot.

Instead of reducing tuition prices, many colleges sought to compete for more students by improving their services--hiring better faculty members, increasing the maintenance of grounds and buildings and expanding student support services, says Arthur Hauptman, a consultant.

As a result, the 1980s saw an explosion in tuition and other charges at the nation's colleges--often several times the economy's overall rate of inflation.

In 1980, for example, the average cost for undergraduate tuition, room and board at the nation's public colleges was $2,422; for private schools, it was $6,570. By 1989, those figures had risen to $5,566 and $15,365, respectively.

At the most exclusive private universities in the nation, the price of tuition, room and board soared to more than $20,000.

Meanwhile, Congress--facing a tight budget at the federal level--has cut back sharply on federal grants, forcing many more students who traditionally have benefited from federal scholarships to rely on student loans instead.

The change has been significant. In 1982, for example, students at 42 of the nation's leading black colleges had amassed about $27 million in student loans; by 1988, that number had almost doubled--to $52 million.