There were a few issues at play here. First of all, Taiwan had a much larger garrison than Hainan at the time. Also, like you mentioned, Taiwan was harder to reach, since the Qiongzhou Strait between the Leizhou Peninsula in mainland China and Hainan is only 19 miles apart. In comparison, the Taiwan Strait is 110 miles. Due to those two reasons, PRC forces invaded Hainan first and most likely would have gone after Taiwan soon after... except Kim Il Sung happened.

Before the Korean War broke out, Stalin told Mao Zedong that North Korea would only be allowed to invade South Korea if the Chinese would support the North Koreans with troops, since Stalin did not want a direct Soviet intervention against the Americans. After the war started, the U.S sent the 7th Fleet to the Taiwan Straights to prevent a Chinese invasion of Taiwan. Since the Chinese could not invade Taiwan with a U.S presence nearby, the troops meant for the Taiwanese invasion were instead redirected to help the North Koreans.

After the Korean War, Taiwan was too well protected politically (since they were then allied to the U.S) and militarily (due to all the fortifications built and troops raised while the Korean War was going on), and the PRC lost their chance.

edit: Another thing to mention is that the PRC had very few ships at the time, so invading Taiwan would take considerable resources. The ships used for the invasion of Hainan were conscripted wooden junks which could make the 19 mile voyage easily, but they could not do the 110 mile trip to Taiwan easily, especially since the KMT (or ROK) had air superiority at the time due to planes based in Taiwan that could very easily sink the ships. Taiwan also controlled important islands in the straights that would have to be occupied by the PRC in order for a full invasion of Taiwan to commence, and, once again due to a lack of air power, the PRC could not attempt that at that time.

Sources:

Chen, Jian, "China's Road to the Korean War: The Making of the Sino-American Confrontation"

Bush, Richard C.; "Untying the Knot: Making Peace in the Taiwan Strait. "

It was a matter of both military and political considerations.

Initially, it was purely military. The reason Hainan fell and Kinmen didn't is because, well, in one place they ROC won the battle and in the other they lost. On Hainan, the ROC lost because of their inability to properly contest the beachheads. Hainan is much larger than Kinmen and the garrison had to cover a much longer coastline, as well as fight a Communist group already fighting in Hainan.

Kinmen is a much smaller island, and was garrisoned by over 50,000 troops at the time of the invasion. Unlike Hainan, where a large garrison was expected and landing sites were carefully determined by probing attacks, the PLA believed that the Kinmen garrison was small and it would easily fall (even more so because it was so close to the mainland). The initial landing at Kinmen was heavily contested, and the garrison was much stronger than expected. The PLA did not attempt to take Taiwan while Kinmen still stood -- it was impractical to sail their impromptu landing vessels past an island that could contest them. Nothing really special about the military stories of either island.

Kinmen has always been the gateway to Taiwan and that's why it's been heavily fortified for decades, and that's why every time the Straits has a crisis Kinmen has been heavily reported on. Taking the heavily fortified smaller island was harder for the PLA in the 1950s and they couldn't take Taiwan without first taking the smaller islands garrisoned by the KMT -- in part because Taiwan is farther away than Hainan is.

And, as you probably know, the reason the PLA couldn't take Kinmen after the 1950s when it was more developed and began to have a real navy is because by 1950 the US sailed the Seventh Fleet through the Straits and ever since then (and the mutual defense treaty of 1954), it has been impossible for the PLA to take Taiwan without involving the US.