I worked for a while on an answer to this question but then lost the text that I've saved. I might eventually re-write it but I can supply some answers, context, and sources to look at.

Chiang Kai-shek wanted to invade mainland China in the early 1960, but was stopped by the US who wanted to maintain the cold war balance. Were the ROC's forces in a state that would have allowed them to compete with the PRC?

This is correct in that Jiang/Chiang always planned to reinvade and not just gain some territory, but to completely wipe out the CCP. However, numerous problems stood in the way:

1. The Kuomintang (Nationalist) army was in poor condition by the end of the Civil War. It was also heavily occupied in suppressing Taiwan's native population and quickly establishing the authoritarian supremacy of the KMT. Realistically, the KMT army was not ready for any major operation off the island until the mid-late 50s, by which point the Korean War had started and the CCP had developed nuclear weapons. The US was tied down fighting Chinese and NK forces in Korea and had little interest in a wider war against China. The PLA had proved a difficult adversary even for the Americans in Korea, and likely still had hundreds of thousands if not millions of troops in reserve to defend China itself.
2. The KMT wasn't that different from the CCP, to be honest. Both were highly patriarchal, authoritarian single-party states with an intense personality cult and essentially no free media or any of the things that we would consider basic civil rights. Jiang's police and military forces on Taiwan imprisoned, tortured, and killed thousands of indigenous Taiwanese as well as liberals and suspected Communists (basically anyone who might not want Jiang to be the Generalissimo). He was also widely held responsible for the loss of the Chinese Civil War because of military incompetence and corruption. The first one is arguable, but he was most definitely incredibly corrupt, living a life of opulence that most Chinese could literally not even imagine. The West was in a double bind. The KMT could not exist without Jiang as it was only held together by his authoritarian personality cult, but it also would never have a chance at re-taking China as long as Jiang was alive bc he was so widely hated by both the Chinese populace and by his foreign supporters.
3. The KMT likely would have found limited support among any mainland population, except possibly in the major cosmopolitan cities where some liberals remained, but again they probably would not have seen the KMT as a huge improvement. During the Second Sino-Japanese War the Nationalists had strategically abandoned large parts of the country and drew the Japanese into urban fighting in major population centers in the hopes that the number of deaths and media outcry from foreign observers would force a peace treaty or lead a major European power to intervene on China's behalf. The Nationalists employed similar strategies during the Civil War, abandoning populations in order to slow the CCP down by having to cope with refugees and cities without functioning services. This strategy arguably worked against the Japanese, but the lost trust of the population was impossible to regain. How would you feel if you knew that in the case of invasion, your country might abandon defending you in order to make you a burden on the invading force, even if it just is the time it takes to execute you? Probably not very safe or grateful. Part of the CCP's appeal was their promise that China would become so powerful it could never be invaded again. A lot of older Chinese today continue to support the CCP based on this, economic growth, and positive initial experiences with Communist recruiters.
4. On that - the Communists did actually enjoy tremendous support in the countryside. Early on, the Communists knew they had to win the support of the people. They built wells, schools for both children and adults, rural electricity, and helped exceptional students study in the Soviet Union to become engineers and scientists. The leadership was extremely strict with punishing any subordinates who abused or stole from villagers. This just highlighted further the KMT's treatment of civilians. KMT only cared much about major cities, during military campaigns they stole from and destroyed villages in order to feed themselves or deny the area to the enemy. Frankly put, the Nationalists (or at least Jiang) cared far more about killing as many Communists as possible than they did winning the hearts and minds of Chinese peasants. If some civilians had to be sacrificed to kill some dangerous Communists, that was just the cost of war. Maybe you can see some parallels to the US failures in Iraq and Afghanistan.
5. Jiang couldn't transport his army back to China, so he was reliant on the US for major operations. When it turned out he could barely defend the barrier islands (Quemoy), the US somewhat understandably was unwilling to fund an expedition to the mainland that would probably have made the Bay of Pigs seem like a like a party on the beach. Jiang did use his remaining amphibious forces to do random raids on the Chinese coast in the early-mid 50s, which accomplished nothing strategically but did kill a bunch of random civilians and make the CCP even more determined to eventually invade Taiwan. Eventually the US did help him transport forces to Thailand and Cambodia to perform/assist with secret operations related to the developing Indochina/Vietnam situation, which seemed to satisfy Jiang. It seemed to matter less to him where he was killing Communists, as long as they were Communists.

Sources:

https://journals.sagepub.com/doi/full/10.1177/186810261804700203

https://www.jstor.org/stable/443798

There was likely not serious intent to Invade

The prior answer ignores the most basic factor in ROC military operations, that the 1954 mutual-defence treaty with the United States effectively limited the ROC to defensive military operations.

In 1953 When the US declared a de-neutralization of the Taiwan strait, Chiang Kai-shek and the nationalists were caught off guard and in no position to attack the mainland. In July 1953, the limited military operation to occupy the Dongshan peninsula in Fujian was a costly failure in which the Nationalists suffered 3,300 causalities. The American MAAG responded to Dongshan by insisting that any future Nationalist operation involving 500 or more troops obtain US approval in advance.

Chiang had alternated between pursuing two forms of US aid in the early 1950s. At times seeking US support for a massive military buildup (costing $1.3 billion) ostensibly aimed at re-invading the mainland. At other times Chiang sought a mutual-defence treaty (resembling the US-South Korea treaty of 1953), expressing several times the ROC was willing to give the US veto power of ROC offensive operations as part of such as treaty.

A mutual-defence treaty with the United States was ultimately signed on December 2, 1954. One of the provisions of the treaty established that “without mutual consent, the Nationalists would not take any offensive action which might provoke retaliation by the Chinese Communists” (Lin 2013). This treaty provision was kept secret to avoid damaging the KMT’s public image, but it unequivocally gave the US veto power over ROC offensive operations.

For similar reasons of maintaining morale and maintaining their public image, the ROC continued to publicly advocate for an invasion of the mainland. Just before the treaty was signed Chiang Kai-Shek announced a new “Planning Commission for the Recovery of the Mainland” and continued to make hawkish pronouncements in subsequent years. The 1960’s saw “Project National Glory” and various small-scale commando actions. But these small operations and loud talk of invasion were intended for the domestic political audience, and I am not aware of any serious intent for a full-scale invasion in 1960. Statements like Chiang’s 1961 New Year’s speech declaring “the Nationalist Army would soon return to save the Chinese people and the world from disaster” should not be taken at face value.

Although Chiang’s hawkish pronouncements were often taken seriously by contemporary global media in the early 1960s, and although the PRC did respond with major movements of troops into Fujian, modern scholarship consistently concludes that Chiang did not seriously intend to invade and was merely trying to obtain specific military aid from the US. In May 1962, Chiang essentially told the US he would invade October 1 unless Taiwan was given “five C-123’s, sixteen B-57 Bombers and 20-25 Tank Landing Ships.” But US diplomats increasingly saw through Chiang’s pronouncements as empty threats. They, like Chiang, were keenly aware that a major ROC invasion would breach the mutual-defence treaty, leaving Taiwan without allies, facing down the PRC.

Military power and likely support on Mainland

I think this part of the question is fairly moot. But there was considerable opposition to the PRC in some places, such as the major revolt in Tibet in March 1959.

But while the CCP's base of support was strained in the early 1960's, the ROC really did not have the force projection capability or sufficient troops to mount a significant invasion of the mainland.

Sources:

• Lin, Hsiao-ting. Accidental State. Harvard University Press, 2016.
• Lin, Hsiao-Ting. "US-Taiwan military diplomacy revisited: Chiang Kai-shek, Baituan, and the 1954 mutual defense pact." Diplomatic History 37.5 (2013): 971-994.
• Taylor, Jay. The generalissimo: Chiang Kai-shek and the struggle for modern China. Harvard University Press, 2009.

i'd also like to link u/hellcatfighter's answer regarding how NRA veterans were treated + the campaign to suppress counterrevolutionaries here: https://www.reddit.com/r/AskHistorians/comments/ihfghq/how_were_the_nra_warlord_and_collaborationist/g30x3ed/