VENICE, Italy (AP) _ President Reagan, urging Western solidarity in coping with world economic problems and dealing with the Soviets, arrived in Italy Wednesday to prepare for a summit of industrialized democracies.

Reagan got a low-key, red-carpet greeting as he arrived at Marco Polo Airport here and was welcomed by Italian Premier Amintore Fanfani. Both the Italian and American national anthems were played.

Before leaving the White House, Reagan asserted that international prosperity and free markets ''are everybody's business'' and called for an end to the trade and monetary imbalances that plague the world's largest industrial democracies.

Reagan spoke just before he left on his 10-day trip, which is expected to be dominated more by tensions in the Persian Gulf and arms control issues than international economic woes.

The president acknowledged that the world's economic powers won't find solutions to all their problems at the summit, but he urged them to make an effort so as not to threaten the prosperity they have enjoyed since World War II.

''We won't find all the answers to those questions about our future at this summit - not by a long shot. ... But we will take steps,'' Reagan pledged.

He said the goal of the meeting is to ''strengthen Western solidarity,'' which he called indispensable to progress on issues dividing East and West.

He advised the industrial democracies to ''move forward to end unsustainable trade imbalances, to reform agricultural policies, and restore stablity to the international currency markets.''

''The major economic powers of the world must also work to eliminate inequities in the international trade environment, to keep markets open and to keep commerce flowing. Economic growth and free markets are everybody's business,'' the president said.

Reagan will meet next week with leaders of Britain, Japan, West Germany, France, Italy and Canada in the 13th such gathering.

Massive imbalances, including record U.S. trade and budget deficits, matching trade surpluses in Japan and West Germany, the plunging dollar against other currencies and the persistent problem of Third World debt will confront the summit participants.

However, analysts and government leaders alike have said that these problems are so thorny that any major new plans to deal with them are unlikely to emerge from the summit.

Still, administration officials vowed that the summit would advance a process of closer economic coordination between the United States and its economic allies put in motion at last year's gathering in Tokyo.

''The question is implementation. So we will go to the summit with the view that we have agreed upon what needs to be done,'' Treasury Secretary James A. Baker III said in advance of Reagan's departure.

Baker said he did not expect the summit to produce any major new initiatives in the areas of currency stablization, trade or Third World debt, claiming the seven nations have already generally agreed to what courses should be pursued.

At the White House, Reagan and his wife Nancy got a sendoff from a group of local high school students, members of his Cabinet and aides who are remaining behind.

The president will spend the next five days before the beginning of the talks at Villa Condulmer, a hotel about 20 miles outside Venice.

Aides said Reagan he would spend much of the next two days dealing with paperwork and consulting with his staff.

The president's original travel plans called for him to spend the rest of this week on a state visit in Rome, but the itinerary was changed because of the collapse of the Italian government and upcoming national elections.

On Saturday, the Reagans will make a day trip to Rome to meet with Pope John Paul II. On Monday, he will move into Venice for the three-day summit talks on the island of San Giorgio.

Shultz has said that during talks with other world leaders, Reagan would underscore the need for an ''adequate force'' to protect Persian Gulf oil shipments from becoming targets in the Iran-Iraq war.

Asked what United States wants its allies to do, national security adviser Frank Carlucci, talking to reporters aboard Air Force One en route to Venice, said, ''We are going out to the allies and making suggestions to them.''

He said the allies have varying capabilities to be helpful and noted that the British and France ships in Persian Gulf.

''What is it we want those ships to do?'' Carlucci asked rhetorically. ''It is as much a presence and coordination matter as much as anything else.''

Carlucci said ''Reagan will certainly be pressing allies for greater coordination, cooperation and support in the Persian Gulf.''

Arms control is also expected to command considerable attention of the Western leaders, but administration officials have sought to minimize its significance as a summit topic.

Regarding expected statement from allies on medium-range missiles, national security adviser Frank Carlucci, talking to reporters aboard Air Force One en route to Venice, said, ''I'm sure that will be discussed. The allies are really very close to a common position on INF. I don't think there are any major differences.''

''I am sure there will be an arms control component (of the summit) statement. INF will be mentioned in that,'' Carlucci said. However, he said the matter will be handled more fully when the foreign minsters meet later next week in Rejkavik.

Carlucci said, ''My position is we need to press ahead on START (strategic arms reduction) talks. There is no reason why the Soviet Union can't decouple this from defense and state and begin to debate and negotiate in earnest for 50 percent cuts. I don't think it will be difficult to get allied support for the draft (decoupling).''

And, while administration officials say they don't expect any new economic breakthroughs, the recent plunge of the U.S. dollar is bound to be a prime topic of discussion - especially in light of Reagan's announcement on Tuesday that he would name economist Alan Greenspan to succeed Paul Volcker as chairman of the Federal Reserve Board.

The plunging currency, which has fallen roughly 50 percent against other key currencies since September 1985, is causing severe economic hardships on export-driven economies like those of Japan and West Germany.

Reagan returns home on June 12, after a short visit to Berlin for the divided German city's 750th anniversary celebration and stop briefly in Bonn.