The issues were familiar -- handguns, vengeance and crime -- but as Washingtonians dealt with them yesterday it was clear that many still were puzzled by the young man who supposedly tried to kill President Reagan.

"You'd think the guy who shot [Reagan] would have been somebody from Nicaragua or El Salvador, but a nice American boy? It's hard to figure," said Vernon Biggs, on the practice green at the exclusive Congressional Country Club.

Especially hard for school children, Pentagon officers, housewives and businessmen to comprehend was why no one can stop assailants from shooting the country's leaders.

"There's an awful kind of helplessness in this country that is supposed to be so sophisticated," said Joseph Macekura, principal of Thomas Jefferson Intermediate School in Arlington.

What most residents of Washington and its suburbs could agree on was that the shooting of Reagan touched their lives as deeply as if he had a relative.

"You may not agree with him or what he's trying to do, but our president is our royalty in this country," said Rena Bozarth, a housewife from Fairfax County. "He represents the American people and shooting him is like shooting a member of your own family."

A common reaction among many area residents was to call their friends and distant relatives to discuss the shooting. Chesapeake & Potomac Telephone Company reported a 20 percent increase in both local and long-distance telephone activity throughout Monday afternoon and into the late evening.

In area schools yesterday, children discussed the attempted assassination and wrote get well letters to the president.

The letters written by the fifth grade class at Belvedere Elementary School in Annandale showed how quickly the six shots fired outside the Washington Hilton Hotel penetrated the consciousness of some of the area's 10-year-old children.

"Dear President Reagan," wrote Jenny Glomb. "Is it true you walked into the hospital? I guess if you did you didn't feel too bad. I saw the tape yesterday on TV. I was pretty upset, so were my parents. Also do you think they should have better security for presidents? Feel better soon!"

Michael Marsh, another fifth grader wrote: "Dear President, I think you shood keep it a secret where you go. And have more gards and make sure that no one has guns."

At Thomas Jefferson Intermediate, the president was roundly praised for his "toughness" after the shooting and for joking with his doctors at George Washington Hospital.

"Reagan has got the people's admiration because of the way he joked on the way to operating room. If you were shot in the chest, would you be as cool?" Julie Barrios, 14, asked of her eighth grade classmates in social studies class. "Reagan just was. It is nice how he got shot and says to himself, 'I got to be cool. I'm president of the United States of America.'''

In other parts of Washington yesterday, there was relief not only that the President survived but that the accused assailant, John W. Hinckley Jr., is not black.

"I'm just glad that it was not a black person, that it was not a poor person," said Steve Blake, a consultant at the National Academy of Science.

Blake's comments echoed the thoughts of other blacks interviewed throughout the city who said they feared that if a black man had shot Reagan, it could have exacerbated racial tension across the country.

In a television interview yesterday morning, Washington Mayor Marion Barry said the attempted assassination will neither hurt the city's image nor affect tourism.

"I think the public understands that this could have happened anywhere," said Barry, pointing out that neither the accused assailant nor the gun used in the shootings was from the District of Columbia. "I mean we've had people assassinated in Memphis, Dallas, Los Angeles and Mississippi. So anywhere you are, people can get access to you."

Many people yesterday said Monday's shooting is part of a growing trend toward violence in the United States, a trend documented yesterday by the Federal Bureau of Investigation's announcement of a 13 percent nationwide increase in violent crime in 1980.

"This sort of thing happens and will continue to happen because we don't enforce the laws quickly in this country," said Richard S. Kotite, a retired U.S. Army brigadier general who lives in Reston. "I come out of this more angry than teary-eyed. I just hope they burn the guy that did it. It is that simple."

At the Congressional Country Club, Republican supporters of Reagan also expressed rage.

"Here we get somebody we can finally believe in, somebody we can really rally around and would do anything in the world for, and they -- whoever they are -- try to take him down," said Lou Bressler, near the first tee. "I'm angry more than anything else."

Bressler's husband, Brower, said news of the shooting made him so angry that he "almost broke [his] TV."

"I supported Reagan, but being Republican or Democrat has nothing to do with it. It's absolutely senseless. Even if it were George McGovern I'd have felt the same way," Brower Bressler said.

At the Pentagon yesterday, several military officers said that while gun control laws won't help stop assassins, better control and surveillance over "kooks" would.

"I thnk the Secret Service should check press credentials more closely and should be more alert about people who get close to the president," said Air Force Capt. Gary Hodsdon of Woodbridge.

With the president likely to be hospitalized for two weeks and not fully recovered for perhaps three months, some area residents speculated yesterday the shooting may hurt Reagan's chances of pushing his proposed budget cuts through Congress.

"Every president has a certain amount of political capital to spend," said Raymond Crowley, a retired Navy engineer who lives in Fairfax. "This shooting is going to put Reagan out of commission at a time when he needs to be in the forefront. He can't go around now up to Capitol Hill and use his considerable talent to persuade."

There were others, however, who said yesterday that the shooting should give Reagan widespread sympathy that could be converted into increased political leverage.

Charles Thomas, an eighth grader at Thomas Jefferson Intermediate, explained:

"Those people in the Congress will pass Reagan's bills because they don't want to put no more strain on the man."