The Carter administration plans to celebrate its new alliance with China in a month-long extravaganza culminating in a coast-to-coast tour by Chinese Vice Premier Teng Hsiao-ping.

The merchandising agenda has become a chief preoccupation of the White House and State Department, generating a whirl of memoranda and meetings by political, press, congressional liaison, security and foreign policy advisers. That agenda includes:

A nationally televised presidential address on U.S. relations with China and Taiwan.

A Washington conference for 600 corporate leaders to discuss the business benefits of the new policy.

The almost certain nomination of Leonard Woodcock as ambassador to China, whth Woodcock's Senate confirmation hearings as the first China policy debate in the new Congress.

Submission on the first day of the 96th Congress of Major legislation to permit continuation of relations with Taiwan on an "unofficial" basis.

A Kennedy Center gala in which top entertainers will perform for Teng, with Certer and the entire Congress in the audience.

A U.S. tour by Teng and his wife, Cho Lin, in which the folksy, photogenic couple will hobnob with Americans in factories, farms and executive suites.

White House plannes hope the Teng tour, sched uled for three or four days at the start of February, will generate the same glow of international amity that resulted from Soviet leader Nikita S. Khrushchev's trip across the country in 1959, when the United States was working toward rapprochement with the Soviet Union.

The vice premier and his wife proved masters of such personal diplomacy last October in a goodwill visit to Japan. The diminutive 74-year-old Teng took that nation by storm. His round face and broad smile were featured daily in the Japanese media and some of his trip was beamed back to China on a live television broad cast.

In addition to a cordial personality, Teng is expected to offer Americans more tangible reasons to be thankful for Carter's new policy toward China. White House planners envision the vice premier's talking Business -- billions of dollars worth -- across the United States: grain purechases in the Midwest, oil service contracts in Texas, machinery and aircraft purchases on the West Coast.

"You're obviously getting int hundreds of millions of dollars of contracts here in Texas alone," said Sen. Lloyd M. Bentsen (D-Tex.), who has been working with White House political advisers to plan a Teng visit to his state.

Bentsen said tentative plans call for Teng to tour a factory near Houston that produces oil-drilling equipment and to discuss pruchases of such gear to develop China's petroleum industry.

The factory tentatively selected is that of Dresser Industries, which has recently sold such hightechnology equipment to China's rival, the Soviet Union.

Both American and Chinese planners are anxious to have Teng visit a Midwestern farm, so the vice premier can take a look at the latest agricultural technology and the Americans can push him to increase Chinese imports of U.S. commodities. But choosing the proper farm poses domestic political problems.

Iowa Gov. Robert D. Ray has been lobbying the White House for a Teng stop in his state, reminding the administration planners that Khrushechev's visit to a farm in Coon Rapids, Iowa, was the public relations pinnacle of the 1959 trip. Some political types here, however, are reluctant to give the plum to a Republican governor like Ray, according to White House officials, and are looking for a safely Democratic Midwestern state to host the farm visit.

The administration is also considering a trip for Teng and his wife to Carter's home state, Georgia. A final stop somewhere on the West Coast seems certain, and there is speculation that Teng might want to visit his old acquaintance, Richard M. Nixon. This prospect cheers the White House, because it would emphasize that the opening to China was initiated by a conservative Republican president.

Political consideration also influenced the tentative decision to have Teng visit Texas. The White House is betting that the good cheer invloved in a personal visit might offset conservative anger about Carter's sudden shift from Taiwan to the People's Republic. "Those things help," Bentsen said. "We'd want to give him a warm welcome, and personal contact can have a big influence on people."

The China campaign is to start before Teng's arrival here on Jan. 29. Carter's speech and administration submissions to Congress are to set foth in detail the administration's rationale for the surprise announcement last month of the change in U.C. policy toward China and Taiwan.

Several hundred chief executives of American corporations are expected to attend a conference here on Jan. 15, in which Secretary of State Cyrus R. Vance, presidential assistant Zbigniew Brzezinski, Treasury Secretary W. Michael Blumenthal and Commerce Secretary Juanita M. Kreps will discuss future relations and trade with China and Taiwan.

One key question to be addressed is how China will finance the large volume of U.S. buying that many businessmen and government officials are predicting. The People's Republic does not have the capital to support major purchases, and some credit arrangements will have to be developed.

The National Council for U.S.-China Trade, an organization of businesses that trade or hope to trade with the Chinese, is arranging the Kennedy Center festivities. Plans are not certain yet, but a council spokesman said "top-flight enertainers" would be featured, and a live television broadcast is a possibility.