G. William Miller, President Carter's surprise choice to head the Federal Reserve Board, may not have the economic and financial background normally associated with the ratified post of central banker. But it is not the first time he has stepped up to an unlikely challenge. That's how he got his job as head of Textron, Inc., the original conglomerate.

Born in Oklahoma, educated at the Coastal Guard Academy where he received a degree in marine engineering and at the University of California at Berkeley where he got a law degree, Miller as a fledging attorney with the Wall Street firm of Cravath, Swaine & Moore was assigned to help Textron founder Royal Little make an acquisition.

Impressed by his ability, Little asked Miller to join Textron for a one-year trial period with the understanding that if he made it, he would make it big. Four years later, at 35, Miller became president of the company which last year had sales of $2.6 billion.

In the intervening years Miller,53, has gained a reputation for acumen and public service within the business community where he is well known as well liked. Outside of the councils of big business, however, Miller is largely an unknown quantity.

The news of his appointment today, to a job that is regarded by some as second in power only to that of the President himself, was greeted by businessmen and others who know him with high priase and predictions that he will prove a tonic for business confidence.

"I think the selection is super," commented Bank of America Chairman A. W. Clausen, who said it was "welcome news to the business community I'm sure." National Association of Manufacturers President Health Larry said it was "one of the finest appointments President Carter has made." He called Miller "One of our nation's truly competent business executives."

House Banking Committee Chairman Henry S. Reuss (D-Wis.) was also enthusiastic. "He sounds great," said Reuss, adding, "His record on making jobs is excellent and I'd like to see our monetary policy focus not just on a stable dollar but also basically positive.

"I think we're dealing with a man not prominent in the monetary field, so there's nothing to get your teeth into," said John H. Perkins, president of Continental Illinois Bank and president-elect of the American Bankers Association. But he noted that Miller has a reputation as "a strong leader" in the business fraternity and predicted "he's going to try to do a good job."

At the same time there was an undercurrent of praise for curent Fed Chairman Arthur F. Burns, whom many in the business community have staunchly supported for his strong antiinflation stand.

"Arthur Burns is a great American n the mold of Gen. George Marshall and Henry Stimson and he will be missed," said Irving S. Shapiro, chairman of the Du Pont Co., and ahead of the Business Rountable. "Given the President's decision not to reappoint Mr. Burns as chairman of the Federal Reserve, we applaud the selection of Mr. Miller."

"I have a high regard for Arthur Burns but we have to recognize that the President has a right to appoint personnel whom he can work with most effectively," said General Electric Chairman Reginald Jones. He described Miller as an "intelligent, skillful businessman, incisive, the soul of integrity, and skilled at personal relationships. He is also an independent fellow who makes a decision known, articulates it, and then sits with t."

"I regret that the President has missed an opportunity to make a major positive contribution to sustaining and improving business recovery by failing to reappoint Arthur Burns chairman of the Federal Reserve Board," said Sen. Jacob K. Javits (R-N.Y.). "we can only hope that Miller . . . will bring to the chairmanship the necessary qualities and policies."

At the annual meeting of the American Economic Association here in New York, the news came as a particular surprise and few were able even to speculate on what kind of monetary policy Miller might pursue as Fed chairman.

"There will be a period of on-the-job training," commented Murray L. Weidenbaum, economics professor at Washington University in St. Louis and a Treasury Department official in the Nixon administration. He said he did not know Miller but called it a "sensible appointment."

Arnold Packer, assistant secretary of labor for policy evaluation, said Miller was "clearly a competent businessman who is concerned over social issues."

One prominent economist who declined to be named said Miller was "a progressive type of businessman," but added "I never thought of him as having any expertise in the monetary field."

However, Miller, among his many positions, is currently a director of the Federal Reserve Bank of B

Besides being chairman of Textron, where he last year earned $191,667 in salary and an equal amount in incentive compensation, Miller holds an array of other official and honorary positions which he will have to give up if approved as Fed chairman, which pays $57,500. Among them:

Chairman of the National Alliance of Businessmen; chairman of the Conference Board, an economic research organization; co-chairman of the U.S.-U.S.S.R. Trade and Economic Council and the Polish-U.S.Council; chairman of a presidential committee to help veterans find jobs; head of the government's savings bond sales committee and a director of Allied Chemical Corp., Conrail and Federated Department Stores.

According to the most recent Textron proxy statement, Miller also holds 68,700 shares in the company, worth approximately $1.8 million at current market values.

Up to now the most public attention Miller has received was in 1974 when for a time Textron - which makes Bell helicopters, Talon zippers, and Homelite chainsaws among its many products - agreed to invest $85 million in financially troubled Lockheed Aircraft Corp.

The unusual investment would have given Textron control of Lockheed, and Miller would have been chairman of both companies.

However, when snags continually delayed completion of the deal it was dropped a year later - just months before the disclosure of Lockheed's multimillion-dollar payoffs to foreign government officials. Miller, in an interview at the time, said he had no inkling of the payoffs at the time.