A new phase of U.S. policy in the Middle East dawned yesterday with the first dramatic departure of Palestinian fighters from West Beirut. Although the broad outlines of future policy are coming into view, administration officials do not expect the details to be announced or even completely settled now, for fear of upsetting the still touchy two-week exodus.

The two immediate priority areas on the drawing boards of American policy makers were mentioned briefly by President Reagan Friday in announcing the dispatch of U.S. Marines to help police the Palestine Liberation Organization withdrawal. They are:

* Lebanon-wide solutions, including restoration of that country's "full sovereignty, unity and territorial integrity," rapid withdrawal of all foreign forces, and insurance for the security of northern Israel.

* Palestinian solutions, which Reagan and Secretary of State George P. Shultz described Friday as being in the context of the Camp David process.

Official assessments indicate that major gains in both these areas are likely to be extremely difficult. U.S. special envoy Philip C. Habib's complicated and time-consuming negotiations on the Palestinian withdrawal may seem simple in contrast.

Shultz, in his news conference Friday, interpreted statements of Israeli Foreign Minister Yitzhak Shamir and Syrian Foreign Minister Abdal Hallim Khaddam as implied commitments to withdraw their respective forces from Lebanon, but U.S. career experts are skeptical of such assurances.

These officials pointed out that the Israeli and Syrian willingness to pull out is conditioned, in each case, by complete withdrawal of the other party.

In fact, Israeli military forces in Lebanon are believed to be digging in for the winter at the very least and perhaps for a much longer stay. U.S. estimates are that Syrian units and the associated Palestine Liberation Army (PLA) will not withdraw voluntarily from Lebanon under existing circumstances.

More likely than a smooth negotiated exodus of nearly 40,000 Israelis and about 30,000 Syrians, in the view of some experienced officials, is a series of blazing battles between those forces in the Bekaa Valley and northern Lebanon.

The Israelis are believed to have the military power to pulverize the Syrians with artillery and from the air, but the Syrians reportedly are digging in.

Heavy Israeli-Syrian fighting, with the United States and Soviet Union looking on as their respective allies battle, would hardly be conducive to tranquility in the area.

As for the internal Lebanese situation, much will depend on the pending presidential election. The only declared candidate, Christian militia leader Bashir Gemayel, is unacceptable to several important Moslem leaders, suggesting the prospect of intensified factional strife in case of his election.

U.S. sources say that Gemayel, who is determined to win the presidency, threatened last Thursday to use his troops to block the first stage of the PLO evacuation unless Moslem leaders agreed to permit his election. For the moment he was forced to back down.

Because of the likely problems ahead, Shultz and other officials have indicated that the United States intends to proceed with diplomatic initiatives on the broader Palestinian issue while withdrawal of foreign forces from Lebanon remains incomplete. "There's obviously some connection between them but they are separate issues," said the secretary of state of the two priority problems Friday.

One obvious pitfall is Egyptian and Arab resistance to negotiating with Israel while Israeli troops remain in Lebanon. Another is that military crises within Lebanon may tend to dominate Washington policy-making at the expense of the Palestinian question.

Shultz' ideas on the Palestinian issue, as suggested by such hints as are now available, include the broadening of the autonomy negotiations for the West Bank and Gaza by the inclusion of widely accepted Palestinian representatives as negotiators for the inhabitants. This was envisaged at Camp David but never developed.

Even without a fresh U.S. determination on this point, direct Palestinian involvement probably would be essential to further progress in the autonomy negotiations. U.S. officials dealing with the problem said Egypt is now much less willing to represent the Palestinians in the negotiations than before the invasion of Lebanon.

A crucial question is Israeli intentions regarding the West Bank and Gaza. So far there is no indication that defeat of the PLO is making the government of Prime Minister Menachem Begin more flexible in the occupied territories. Defense Minister Ariel Sharon wants to settle those territories with Jewish strongpoints at an intensified pace, and Begin reportedly wants to annex them when the time is right.

If these attitudes persist, Shultz' ideas are likely to meet strong Israeli resistance. Shultz, saying he was quoting Reagan's views, spoke out at his news conference against expansion of West Bank settlements. But such statements from Washington have done nothing to deter Israeli settlements policy in the past.

Regarding the future of the Palestinian movement, U.S. intelligence is already reporting efforts to create new centers of leadership on the West Bank, in Syria, among the remaining Palestinian masses in Beirut and elsewhere in the Middle East. PLO Chairman Yasser Arafat, who is believed likely to go to Tunis, may find it more difficult to control an even more fragmented Palestinian diaspora.

Some emerging leaders may be relatively moderate, but others are likely to be radical. Moderate Arab governments fear further radicalization of Palestinian elements, which is among the reasons for keeping their distance from the United States.

Some intelligence reaching Washington suggests that the recent explosions in France are a first wave of a new round of Palestinian terrorism, under the same provocative faction that struck the Israel ambassador to Britain, Shlomo Argov, outside a London hotel June 3. That action turned out to be the trigger mechanism for the Israeli invasion of Lebanon 11 weeks ago, whose consequences for the Middle East and for U.S. policy in the region are still developing at a rapid pace.