President Carter flew to the sealed-off mountain retreat of Camp David yesterday to begin final preparation for his personal effort to bring the leaders of Egypt and Israel together on a plan for peace in the Middle East.

Before departing by helicopter from the South Lawn of the White House on the 65-mile trip, Carter sought to dampen public expectations for the outcome of his summit meeting with Israel's Menachem Begin and Egypt's Anwar Sadat. "The prospects for complete success are very remote," a somber Carter told reporters.

Begin and Sadat will arrive separately this afternoon at Andrews Air Force Base and fly directly to Carter's 200-acre hideaway in Maryland's Catoctin Mountains. No deadline has been set for the summit talks, the most important presidential intermediary effort since Theodore Roosevelt sponsored the Portsmouth conference that ended the Russian-Japanese war in 1905.

With Begin and Sadat arriving without being able to agree publicly even on what the conference is intended to achieve, Carter did not minimize the difficult task confronting him.

He will begin the conference by trying to lower the tensions that have arisen between Sadat and Begin and to lessen distrust of American intentions both men share. U.S. officials have repeatedly emphasized that the key to the summit will probably lie in the personal interaction of the three leaders as they chat first informally and later about substance.

The way the three spent the final hours of preparation for the week or more of near total isolation from the world - and often even from their closest aides - illustrated their differing often conflicting, temperaments and concerns.

For professional politicians, the three are surprisingly sensitive to rebuffs and are quick to interject emotion into policy matters. Their Triangular talks and contacts, set in motion by Sadat's impulsive trip to Jerusalem last November, have risen and fallen to a large extent on personal reactions that have ranged from euphoria to deep hostility.

Begin arrived in New York Sunday and devoted yesterday to resting at his hotel, where he met privately with members of the American Jewish community throughout the day.

Begin's rough - at times inflexible - responses to the peace moves this spring alienated some members of the U.S. Jewish community as well as provoked a diplomatic standoff with Carter and a rupture with Sadat. Begin refused to mask with diplomatic niceties his fundamental belief that Israel would never withdraw from the West Bank territory of the Jordan River.

But American Jews were reportedly instrumental in convincing Begin in recent months that he had a serious image problem in the United States and that he should become less combative in appearance in public and stress flexibility.

His quiet contacts yesterday seemed designed to balance the importance he attaches to support from American Jewry going into the conference and his desire not to flout Carter's strong requests for an embargo on presummit publicity.

Sadat, meanwhile, spent the day in Paris and dined last night with French President Valery Giscard dEstaing, a key figure in the Egyptian president's strategy to keep an international option open if his peace initiative and the Camp David summit fail.

If that happens, Sadat's first move is likely to be to take the Middle East conflict back to the United Nations to seek condemnation of Israel for intransigence on the West Bank, Egyptian sources indicate. Other topics likely to have been involved in the Sadat-Giscard talks are the chances for new pressure by Arab oil producers on the industrialized world if the talks fail, and eventually more French arms sales to Egypt.

Before leaving Egypt for France, Sadat dramatically labeled the summit "a last chance" for peace. Rejecting a comment by Begin that negotiations growing out of the summit could go on for months, Sadat said, "I say not to long, drawn-out talks."

In New York, Begin returned to the subject. "We will strive for an agreement at Camp David which will make it possible to continue serious negotiations to establish throughout the Middle East a final peace."

This long-distance exchange captured much of the difference between the two men and illustrated the difficult task Carter has chosen for himself.

Israelis who know Begin and who have watched him make political decisions describe him as a plodding stickler for detail who breaks even small problems down into the most minute components, examines each segment independently, goes back into his finely developed sense of history to look for support for his argument, projects the likely effect of his decisions far into the future and only then makes up his mind.

"For Begin, placing a comma in an agreement on the West Bank is like building a skyscraper for most men," says an American who has dealt with him.

This time-consuming process is clearly frustrating for Sadat, a visionary who detests detail work. He has repeatedly stunned the world with audacious decisions that leap over existing barriers to create entirely new situations.

The 65-year-old courtly Israeli prime minister has been seriously ill for much of the year. But during Secretary of State Cyrus R. Vance's visit in July, Begin appeared to be in good health and good spirits.

Israeli sources suggest that Carter is likely to get more movement from Begin by trying a friendly, sympathetic approach than by repeating the attitude of confrontation he adopted in March when Begin brusquely refused to show any flexibility on the West Bank issue. Carter is believed to have studied psychological profiles of both men that drew in part on Central Intelligence Agency assessments of their character and personality.

While Begin met American Jewish leaders and Sadat saw the French president Carter sought an extra day of the seclusion he thinks is vital to the summit, and which he seems to increasingly enjoy.

"We will be almost uniquely isolated from the press and from the outside world," Carter said as he left the White House. "My hope is that this degree of personal interchange, without the necessity for political posturing or defense of a transient stand or belief, will be constructive.