Which US administrations in the 20th century are most important in terms of US-China relations?

(Found out OP's repost so this answer is also a repost...)

I am assuming you're talking about the recent Sino-US trade war that's been going on and off. This post would focus on events between 1949-1990s. Since the watershed moment of Sino-US relations came in 2018, I would have to leave that bit off completely. But I will give a bit of historical context to how the relationship between the two great powers changed during the Cold War. As we will see, trade relations between the two are more dictated by politics above all else, and no one administration has the "final say" or "greatest influence".

1949 - 1972, Confrontation

Initially, Washington was not very hostile towards the communists taking over the mainland. Then US ambassador John Leighton Stuart was instructed to stay in Nanking on April 1949 when the former Nationalist capital fell to the PLA (the Soviet embassy followed the KMT south to Canton instead). However, as the Korean war broke out and the two Taiwan strait crises enveloped the region during the 1950s, relationship quickly soured and the United States did not hesitate to contain the new communist threat. The main US strategy at the time was "containment", first proposed by George Kennan in 1946 with his "Long Telegraph" to counter the Soviet Union. By 1950 however, a strategic report called NSC-68 released by the US National Security Council had changed things quite a bit. It advocated for military methods as the primary means for the strategy of containment. Against Communist China (and USSR since it was still an ally in the 1950s) such alliances would include:

ANZUS (1951) - an alliance including USA, Australia and New Zealand that covers the Pacific area

Treaty of Mutual Cooperation and Security Between the United States and Japan (1951, amended in 1960) - a military pact between USA and Japan

Mutual Defense Treaty Between the United States and the Republic of Korea (1953) - same as above but applied to South Korea

Sino-American Mutual Defense Treaty (1954) - An military alliance with the *Republic of China* (don't confuse with Beijing)

Southeast Asia Treaty Organization (1954) - Think of it as a South East Asian version of NATO (notably this alliance has Aus, NZ, UK and France and excludes French Indochina)

Well you might ask, what about trade relationships? Since USA and communist China had no diplomatic relationships at the time, there were no formal economic activities to say about. Further more, the US had applied an economic and technological embargo on Red China. Through the Coordinating Committee for Multilateral Export Controls (CoCom), the western bloc countries would apply that embargo to not just Soviet Union and China, but all Comecon countries. However, the Communist government could smuggle goods and/or technology from Hong Kong and Macau, then under British and Portuguese rule respectively.

The point is, in the middle of the 20th century, the US used military methods to deal with China first and foremost. Economics and therefore trade took a back seat.

1972 - 1989, Honeymoon

After the Sino-Soviet split that estranged Red China from the Communist bloc and the surprise visit of Nixon to Beijing, relationship between the two powers. The same year both countries signed the Shanghai communique. US trade embargo to China had been ended by Nixon a year before. By 1973 the Nixon administration even approved the export of Inertial Navigation Systems (think GPS before GPS) on Boeing 707s sold to mainland China. The limitation of technology exports to China would continue to unravel until the Reagan administration. By 1979, China and the US had established full diplomatic ties. In 1980, the US Congress allowed the US government to give China a "Most Favored Nation" trade status that would eliminate high tariffs Chinese goods would face at US customs. Coupled with economic reforms implemented by the new ruler Deng Xiaoping during the late 70s, by 1984 the USA became the third largest trading partner of China. However, this by no means suggest the US "saved" the Chinese economy (as suggested by Donald Trump) because during the 1980s and the 1990s, China mainly attracted investments from Hong Kong, Taiwan and Japan for its growing manufacturing industry.

As we can see the changes to US-China trade policy straddled several US administrations and no one government had "key influence" per se on this policy. It is more useful to think of these administrations (from Nixon to Reagan to whatever) as a collective US leadership. Because while domestically Republicans and Democrats would bitterly fight on everything, in the case of foreign policy, there exists a general direction/strategy that US administrations would more or less keep consistent.

1989 - 2001, Contact

Many people would think the Tiananmen Square incident drastically changed US-China relationship. While this was true, a more fundamental factor had resulted in this change. The US won a stunning victory against the Soviet Union in the Cold War. Had the US won the Cold War but incurred substantial losses, China could exploit any arising opportunities. But not only had the USSR collapsed, the US used this chance to expand into Soviet sphere of influence (think NATO expansion). In this setting, China had lost its value as a counterweight to Moscow in the eyes of Washington.

The new strategy the Clinton administration had regarding China was one of "contact". The hope was if China could continue to reform and develop its economy then the resulting prosperity would catalyse democratic changes. Under this assumption then Secretary of State Warren Christopher visited China in 1994 and promised to "de-link" human rights issues with trade. When China's General Secretary Jiang Zemin visited the US in 1997, the Sino-US relationship was described as a "constructive strategic partnetship". This strategy would culminate in China joining the WTO in 2001.

That's as far I could go without violating the strict 20 years rule of this subreddit. However, if you want to ask me about USA's global strategy that does not touch on the 20 years rule (generally) then I am happy to post another comment.