For months, Kathy Ashton's fiance, a Fairfax County police officer, tried to persuade her to learn to shoot his .38-caliber revolver for self-defense.

At first, Ashton, a 26-year-old computer programmer for the Securities and Exchange Commission, balked. But, the more she thought about the nights she would spend alone when her future husband was working, the more she concluded it might be a good idea.

Last week, Ashton took a three-hour, $25 course at a Lorton range, where she fired .22-caliber and .38-caliber revolvers, joining the ranks of homeowners nationwide who are learning to shoot handguns.

National Rifle Association spokesman Andy Kendzie said 60,000 people across the country have taken NRA gun familiarization courses since the group began offering them three years ago. About 60 percent of those taking the courses are women. "In the last year, many, many classes have had 100 percent women," he said.

Virginia and local officials say there is no record of the number of handguns in the state because gun registration is not required, except for fully automatic weapons such as machine guns. But the NRA says 40 to 50 percent of U.S. households have guns and that in one of every four homes there is a handgun.

At the Gilbert Small Arms Range in Lorton, one of three public ranges in the immediate area, an increasing number of "regular homeowners" are learning to shoot handguns, said Frederick L. Williams, president of Gilbert Security Service Inc., which operates the range. About 25 to 30 percent of people who sign up for his Monday night gun familiarization classes have never before held or fired a gun, Williams said.

The shooters are grandparents as well as children as young as 9 or 10. There are usually more women than men, probably because they are more likely to admit they do not know about guns, said range officials. The four persons in Ashton's class are women.

One of them, Catherine LaTour, 37, a management analyst for the Department of the Army, took the course to learn more about her husband's automatic pistol, and how to keep it safely away from the couple's 2-year-old son.

"Also, I've always been scared about somebody breaking into the house," she said.

LaTour was so enthusiastic after an hour of firing .38s and .45s that she now dreams of someday becoming an expert shot.

"I was just so wound up when I got home," she said. "I stayed up until 11:30 telling my husband all about it. I just really enjoyed it."

Maryland Small Arms Range in Forestville offers basic self-defense pistol classes to the public every Wednesday. Manager John Pepper says the classes are limited to three or four people and that about 60 percent of his students are women.

The third range is the Small Arms Range in Annandale. It offers classes only to police, but the public can shoot there.

Local gun experts say it is a good idea for new gun owners, or those with rusty skills, to take any of the area's gun safety and familiarization courses, such as those offered by a range like Gilbert Small Arms or the NRA.

They disagree, however, about whether owning a handgun for self-protection is smart. Brian Moe, training director for Gilbert Security Service Inc., cautions against handguns for homeowners who, unlike LaTour and Ashton, are not interested in practicing.

If the average homeowner insists on having a gun, Moe recommends a shotgun instead. It's more cumbersome but deadly at short range. "The shot pattern is big enough to cover the hallway in most homes," but the pellets are less likely to travel through walls and furniture, he said.

Moe, a former captain with the Fairfax County Sheriff's Department, also says the mere appearance of an unloaded shotgun or the "ker-chunk" noise of cocking such a gun would be "extremely intimidating" to an intruder.

He warned strongly against keeping loaded guns around the house, even if stored on a top shelf. "Kids are curious about everything," Moe said. "They'll say, 'What is it that my parents have up in that closet that they don't want me to see?' "

Fairfax prosecutor Robert F. Horan Jr. questioned why anybody would want to own a gun for self-defense in Fairfax County, "which has to be one of the lowest crime counties in the United States."

"In most instances," said David Russell, a Fairfax County police spokesman, "you wind up shooting either a family member, the paper boy or you become a victim yourself simply because you're not prepared for the confrontation.

"You have on your mind a scenario that will probably never occur because things just don't happen the way you think they will, the way you envision it on TV or something."

Mark Shulimson, a spokesman for The National Coalition to Ban Handguns, says he has no objection to controlled range shooting. "But we feel the handgun is not an acceptable self-defense weapon," he added.

According to coalition figures, handguns are responsible for 22,000 deaths a year. In 1983, the group said, 12,000 of the deaths were suicides, more than 9,000 were homicides, and an estimated 1,000 were accidents.