After achieving a modest increase in decorum at his first presidential news conference by asking reporters not to shout for his attention, President Reagan will try for an even more decorous second session by calling on preselected reporters to ask the questions.

Before the news conference, those reporters permitted to ask questions will be chosen by lot. The president will call out their names in order.

In addition to experimenting with the format of the presidential news conference, Reagan plans to hold less formal weekly meetings with groups of reporters, sometimes with cameras presents and sometimes without. He will hold a formal news conference no less often than once a month, White House press secretary James S. Brady said yesterday.

All of these methods of handling contacts between the president and the news media are suggested in a report presented to the White House this week.

The report is an attempt by a number of former government officials and White House correspondents to suggest ways to improve the relationship between the chief executive and the crowd of reporters assigned to cover him.

Its recommendations have been acted upon with a speed not usually seen in connection with reports of private groups submitted to the White House. That speed indicates that Reagan and Brady are eager to shake up the existing system.

The suggestions have been advanced in other administrations, but what is new is that they are being taken seriously by the Reagan team.

Brady said yesterday that Reagan was pleased with the format of his Thursday news conference. Most of the White House reporters also were content with the quieter atmosphere achieved by their remaining seated as they raised their hands to ask questions. In the past, reporters leaped to their feet and shouted, "Mr. President, Mr. President," while waving their hands in an effort to attract the president's attention.

The television and wire service reporters who have been guaranteed an opportunity to ask questions in the past are not pleased, however, by the prospect of a lottery.

Brady rebuffed a number of complaints yesterday saying: "I don't think the republic will stop if we try this one-time experiment."

The complaints centered on the possibility that a lottery will give the chance to ask questions to reporters who do not usually cover the president, but drop by only for major White House events.

"It will probably please no one," Brady said, but insisted that he is committed to trying a lottery.

Former president Ford used a lottery system, but only for news conferences he held while traveling away from the White House.

The changes in the news conference format have been announced as rumors swept through the White House press corps that the Reagan administration was going to institute a dress code for reporters and television technicians who work at the White House.

Brady said he had no knowledge of an impending dress code.