There are a couple of different factors that were at play some of which were ideological and some of which practical. First, let's consider China's decision to side with the Soviets, a policy you'll sometimes see referred to as China's "Lean to One Side", after a speech of Mao's. Reasons of ideological purity aside, the alliance with the USSR offered China significant benefits from the perspectives of China's international security and economic security. For one thing, allying with the Soviet Union lessened the threat that the USSR itself might have posed to China. Russia is large country with a long land border with China and a history of confrontation with China. An alliance with the Soviet Union helped alleviate the threat of potential future conflict. The alliance also helped ensure China’s military capability to respond to threats from the US. The new treaty Mao signed with Stalin in 1950 included increasing military support to China and providing air defense installations for coastal China.

The alliance also brought significant economic benefits to China, including a natural trade partner with Russia during a period when the US ‘containment and isolation’ policy cut off potential trade with much of the rest of the world. This is an important point, because willingness to engage cuts both ways. At this point, the US was actively seeking to isolate China. The Soviet Union also provided significant economic support, sending advisors and technicians, providing a development model for China to follow as well as providing development loans. More than ten thousand engineers and administrative advisors went to China from the USSR and Soviet projects in China represented fully 3% of state investment in China’s first Five Year Plan.

Despite these obvious benefits, the Sino-Soviet relationship was plagued from the start. For one thing, Mao found the Soviets to be unreliable allies. While Mao continued to consult Stalin on a great many matters, he was obviously bothered by what he perceived as insufficient support from his ally. During the Korean War, Mao did not receive the Soviet backing he had expected, which strained the relationship somewhat. A similar situation would play out with Stalin’s successor Khrushchev with regards to Soviet support during the Taiwan Crisis in 1958 and with the Soviet’s reneging their promise to provide China with plans for nuclear weapons. In all of these instances, Mao felt that the Soviets had to some extent betrayed him. In addition, Mao, perhaps being overly suspicious, came to perceive signs of Soviet influence and overreach into Chinese affairs. For one thing, years of Soviet advisors and training for Chinese cadres had created interest groups within China that seemed beholden to the USSR and were harder to control. Mao felt that as senior a leader as defense minister Peng Dehuai was overly loyal to the USSR and when Peng criticized the Great Leap Forward, Mao felt the criticism came from Moscow and had Peng purged. Then too, Mao viewed Khrushchev’s proposals for a joint fleet and the building of long range radio facilities in China as extensions of Soviet control in China and perhaps even violations of Chinese sovereignty.

A couple of events brought the situation to a head and led to the Sino-Soviet split in 1960. One was Khrushchev's "secret speech", which he delivered at the 20th party congress in 1956. In it, Khrushchev denounced Stalin for creating a cult of personality. The speech upset Mao for a number of reasons: he hadn't been asked to approve the content, or even informed of the speech and Chinese delegates were locked out of the speech when it happened. Mao might also have worried because many attacks Khrushchev had leveled at Stalin could easily have been leveled at Mao. At this time, there were ideological cracks starting to show in the relationship as well; Mao formulated his notion of 'continuous revolution' and wanted a giant push towards communism (see, the disastrous Great Leap Forward), the Soviets had different advise.

At this time, the Soviets were also suggesting a number of joint military projects, including a Soviet pacific submarine fleet and, in order to keep contact with the submarines, long range radio towers that would be on Chinese land. Mao at this point had already become very suspicious of Khrushchev and viewed these suggestions as possibly infringing on Chinese sovereignty. In 1960, the USSR terminated its aid projects to China. In 1963 Mao published his '9 critiques' of the USSR, a blistering attack on Soviet 'hegemonism' and 'imperialism'.

Now, here's the crux of your question. Note, that the Sino-Soviet split happens fully 10 years before the thaw in US-China relations. In that time, Sino-Soviet relations went from tense to outright hostile. The Soviets built up their military and under Brezhnev started to encircle China: buildup of the Soviet Pacific fleet, the USSR strengthened its relation ship with North Korea, the Soviets were supplying close North Vietnamese allies and they built up troops all along China's long border with the USSR, which at that time was not just Russia, but included some Central Asian states that are now independent. At its height, the deployment of Soviet forces along the Chinese border was 50 divisions. The Chinese did not view it as a defensive deployment. To make matters scarier, Brezhnev demonstrated he was willing to intervene into other, supposedly independent, communist countries. There were border clashes between Chinese and Soviet troops in 69 and 71.

So that's the environment during which the Chinese-US thaw occurred. China now saw the Soviets as the primary threat, not the US. In that regard, the US was the natural ally. Mao expected, and correctly so, that he could balance against the Soviets with US support. He also hoped to find a resolution to the Taiwan issue, although that proved to never come.

There are two great sources you might look into. One is China's Search for Security By Nathan and Scobell, which isn't really a history book, but an international/foreign policy book about China's foreign policy. There is one chapter which describes the China-USSR-US history though about as well as is possible. For a more in depth look (including some fascinating stuff about disagreements and tensions between Mao and Stalin) I also recommend Mao's China and the Cold War by Chen Jian.

And for a followup: Why did the US support China over the USSR if China was initially more hostile?