When John Paul Getty died last June, he left an unexpectedly huge chunk of his estate to a little-known art museum hanging over the crests of Malibu. The art world, particularly on the West Coast, may never be the same.

The will bequeathed $720 million in stock to the Getty Museum, and since then high-level staffers have been walking on air and gasping at almost limitless vistas. "We are still in the late stages of shock," admits Gillian Wilson, the British curator of the museum's extensive decorative art collection. "I guess we are still all walking around with our eyes popping out of our heads."

Already, word of the windfall has attracted some artful opportunists to the 10-acre museum by the sea. One Texan offered Wilson a Chinese vase for just $20 million. "I wrote his back and told him he was off his rocker," Wilson says, a smile breaking through her reserve. Another citizen, she adds, recently tried to sell the Getty an old boot as a priceless relic.

Faced with the prospect of trying to maintain sanity at the opulent museum, which looks at first glance more like a Roman villa than the site of a well-regarded art collection, is Stephen Garrett, the newly appointed director. Garrett, 54, a product of Cambridge University, insists that he and his fellow workers are taking their huge endowment in stride. "It's hasn't made me nerous," he says, doodling on a scratch pad. "It simply makes me feel the museum has a great responsibility. You feel honored and slightly awe-struck.

Although probate proceedings may hold up the will for three or four years, Getty staffers are already planning how to budget their vast fortune. Garrett, a long-time Getty protege, maintains that the museum will continue along the conservative lines established by its benefactor.

No friend of the modern arts or modern artist, J.P. Getty was an oil magnate who craved the classical and built his museum's $50 million collection in just three areas - Greek and Roman antiquities, 18th-century French decorative arts, and paintings of the Baroque and Renaissance period.

Even in choosing the design for the museum's building, Getty shunned modernity. Having made billions in industry, he remained unimpressed with the steel-and-glass world he helped create. Instead, Getty chose to build his museum as a replica of a Roman villa on 10 acres above the Pacific. Critics from London to Los Angeles ridiculed the building when it opened in 1974, but the museum's Mediterranean-and-classical character was firmly established.

"It would make sense for us to build on the foundation we already have from him," Garrett says. "Our major concern over the next 10 years will be simply to improve our collection." This policy comes as no surprise, since the museum's board of directors is dominated by loyal Getty Oil, is chairman of the museum board. The vice-chairman and treasurer is Norris Bramlett, who for 28 years served as John Paul Getty's grim-faced personal assistant.

But the enormity of the endowment may yet widen the perspective.As the will passes out of the probate courts the Getty will become, suddenly, one of the financial giants of the art world. The Getty Museum's endowment, for example, is six times that of New York's Metropolitan museum of Art.

Some of the money will surely fund new acquisitions, and each curator is breathlessly awaiting the day when he can swoop down on some long-coveted, high-priced purchase. "It really was terrific of the old man to leave us all that money," says curator Wilson in her rapid-fire Londoner's English. "After we got the news we all went back to our rooms and made long shopping lists."

Dampening the euphoria, however, are some of the harsher realities in today's highly competitive art market. If the museum becomes too loose with the checkbook, it could inflate prices paid by Getty curators. "The more we go out showing rolls of dollar bills, the higher the prices will be for everyone, including us," explains Garrett.

A more serious problem, however, begins with the simple logic of history. Getty's museum, originally opened in the 1950s, is hardly a venerable institution compared to the Met or the British Museum. Yet because of Getty's limited tastes, his museum specializes in art that long ago was garnered by other museums and wealthy individuals. With more than $700 million to spend, the Getty curators find themselves with very little left to buy.

"We're late in the day," Garrett admits, scratching his hair. "The great museums of Europe have been in existence and we'll never catch them. The Met has been around a lot longer than us."

So despite their millions, the Getty people are worrying about a problem most museums would love to have - what to do with a vast sum of money. Some interesting ideas are being explored, such as, most notably, turning the Getty into a major educational and cultural institution. Garrett speaks of Getty sponsored television specials and movies focusing on the classical arts.

"Maybe there are ways we can help bring an interest by using new techniques," he says, wondering how to appeal to the Southern California public. "When one thinks about the time spent by Americans watching television as opposed to going to museums, you have to try something different."

Fitting the museum into the mainstream of Los Angeles may prove the greatest challenge. Never before has so well-financed a cultural institution tried to establish itself on the West Coast. And indications are it won't necessarily be a smooth process.

Getty staffers have fears about their museum turning into a silly, classical Disneyland. They fear the ridicule of their European and East Coast counterparts who still insist Los Angeles is nothing more than a set for a great big movie. "Their supposition is that every umemployed stage hand in Burbank came here trying to put up a set for Spartacus or something," Garrett complained. "People think this is frivolous, pastiche and second rate."

Even while worrying about opinions in London or New York, most Getty people - including the many Europeans - consider themselves fortunate to be able to help create a major development in a city still culturally wet behind the ears. "Los Angeles," observes Steve Garrett, "is a very fertile, imaginative, inventive place. The challenge of bringing the heritage of the centuries to a place where the atmosphere is so new and often so trashy is simply explosive."