Washington — Still fresh and unscarred after doing minor combat with a few US senators, George P. Shultz now faces the big battles.
Answering senators' questions about his business connections and Middle East views has been the easy part for Shultz. Senators have given the tanned and unflappable secretary of state-designate mostly high marks for his two-day performance before the Senate Foreign Relations Committee.
Shultz would at this point probably appreciate a breathing spell to take his bearings. But he faces a world in turmoil, and the world will not wait. Rarely has a new secretary of state had to deal with so many upheavals occurring in so many places around the world.
In almost every case, the options open to the United States are not easy ones. In only one case does a clear-cut success for the administration now seem possible: resolution of the conflict in Namibia, or South West Africa.
In some cases, the US has considerable potential influence over events, such as the Lebanon crisis, or in the matter of strained relations with America's European allies over the question of East-West trade. But even in the latter case, the US has tied its future moves on East-West trade to developments in Poland, which are largely beyond American control. When it comes to one matter to which Shultz must give immediate attention - Iran's invasion of Iraq - US leverage is extremely limited.
In none of the crises facing Shultz is a clear and immediate threat from the Soviet Union involved, despite the Reagan administration's initial fixation on Soviet activities.
In addition to fighting innumerable battles on all of these foreign fronts, Shultz will inevitably face struggles on the home front over foreign policy decisions. One such pending decision: how to deal with arms sales to Taiwan and conservative pressure on the issue from Capitol Hill.
Shultz will also have to fight against ultraconservative pressure aimed at placing more ''Reaganauts'' in positions of influence at the State Department. Just as Secretary of State Alexander M. Haig Jr. did, Shultz is expected to want to place old associates as well as professional foreign service officers in a number of key positions.
But for Shultz the lead problem is Lebanon, with other problems pressing in close behind it all the way from El Salvador and Argentina to more distant China. Here is the world as he might now see it in order of hottest priorities:
* Lebanon - The Palestine Liberation Organization (PLO) seems to be stalling, postponing its departure from Beirut in the hope of making political gains, possibly including a US agreement to direct talks with the PLO. Shultz, in his Senate hearings, made a gesture toward the PLO by not ruling out a role for the organization when it came to possible negotiations over the future of the West Bank and Gaza. He placed much greater stress on the Palestinian question than did Secretary Haig. But it is not clear that, having accepted a pattern of reacting to events in the Middle East, the Reagan administration can now take the lead that Shultz seems to desire.
* Iran-Iraq - Iran's thrust into Iraq places the US in a difficult position, where the potential threat to oil-producing nations in the region is not matched by an American ability to influence events. White House officials have announced US opposition to the Iranian move. But at the same time they concede that the US does not want to close the door completely to future contacts with a country as important as Iran. Reagan and Shultz are to meet July 20 with the Saudi Arabian foreign minister. The US is reviewing ways to help bolster Gulf defenses in case the Iranian invasion ''spills over'' into the other oil-producing nations in the region. The Saudis also want progress on the Palestinian issue.
* US-Europe relations - State Department officials believe that US relations with its Western European allies are now at their lowest state since President Carter zigged and zagged on the neutron warhead decision four years ago. When British Prime Minister Margaret Thatcher goes public as she has, with complaints about a decision made by Reagan, one can be sure that the trouble is serious. Reagan's decision to block equipment going from American subsidiary companies to the Soviet-West Europe gas pipeline struck the West Europeans as heavy-handed interference in their affairs. Shultz, an old friend of West Germany's Chancellor Helmut Schmidt, has the background needed to patch things up. Shultz himself is opposed to trade sanctions on principle but he must go along with the man he describes as ''the boss,'' President Reagan.
* Grain - The West Europeans accuse the US of double-dealing by urging trade sanctions against Moscow while continuing to sell grain to the Soviet Union. Shultz has come out in opposition to any long-term grain agreement with the Soviets. The time to negotiate such an agreement is nearly here, given the Sept. 30 expiration of the old five-year pact. Secretary of Agriculture John Block is urging a deal under which the Soviets could buy as much as they want. A presidential decision is expected soon.
* Latin America - Shultz seems determined to continue with the administration's push for more military and economic aid to El Salvador and other Central American nations. But Reagan's Carribean Basin economic initiative and Salvadoran aid plan are under attack in the Congress. Argentina, meanwhile, seems interested in reestablishing ties with the US and forgetting the Falklands strain. The US has a chance there for ''creative diplomacy,'' experts say.
* China - Haig recommended that Reagan go a long way toward agreeing to Peking's demands that the US end arms sales to Taiwan. His advisers are reluctant to go as far as Haig wanted in this direction, but at the same time fear a disruption of relations with Peking.
* Namibia - Critical negotiations begin in New York next week, and State Department officials think the chances for resolving this lengthy conflict involving South Africa and several black African nations are better than ever before.