The war was a long time in the making. The 1937 Incident - generally called the Marco Polo Bridge Incident in English history books - is regarded as the formal start of the Second Sino-Japanese War, but as a matter of fact, the Japanese Empire and the Republic of China had already been in a low intensity war ever since the establishment of Manchukuo. To wit, several "incidents" preceded the Marco Polo Bridge Incident:

• The Shanghai Incident of 1932, in which Japanese forces, in response to an anti-Japanese riot in China and the massing of Chinese military forces outside of Shanghai, invaded, bombed, and occupied Shanghai until the situation was finally diffused by international diplomacy.
• The Rehe Incident of 1933, during which Japanese forces attacked Chinese military forces in the province of Rehe on the basis that Rehe belonged to their puppet state Manchukuo, and subsequently upon victory, annexed it.
• The Suiyuan Incident of 1936, in which the Japanese Kwantung Army instigated the Mongolian prince Demchugdongrub to declare Inner Mongolia's independence from China, which led to a short proxy war in which Demchugdongrub was ultimately defeated by the Chinese general Fu Zuoyi.

Thus, we can see from the above sequence of events that China and Japan were already skirmishing, but that neither governments were willing, as of yet, to engage in full-scale war. The key to understanding Japanese policy at the time was that the Japanese perceived the Chinese as a weak, divided people who they could extract concessions from without resorting to total war which, naturally, carried a risk, especially given the possibility of European and American intervention, and especially given the increasing threat posed by the Soviet Union.

Their strategy depended on a combination of small-scale operations, threats, and political ultimatums, which were designed to slowly but steadily expand Japanese interests and control in China, one step at a time. They were not unsuccessful - almost every time, the Chinese chose to compromise, and the signing of the Tanggu Truce, the He-Umezu Agreement, the Chin-Doihara Agreement, etc. all benefited Japanese expansion in China, or outright signed Chinese territory into Japanese hands. The Marco Polo Bridge Incident only contributed to this success, as it allowed the victorious Japanese to now occupy Beijing and Tianjin.

To this end, public and military sentiments were building within China that, enough was enough. The Republic had to make a stand against Japanese extraterritorial expansion in China - or die a slow death. This ultimately culminated in Chiang Kai-shek's famous "limits of endurance" speech, in which he committed to expelling the Japanese from northern China, and followed through by laying siege to Japanese military forces in Shanghai. On the side of Japan, communications evidence indicates that the Japanese high command was initially reluctant to escalate the war. As mentioned above, their relatively low risk strategy for expansion was already working, so they had no reason to commit to a costly full-scale war. However, as Chinese resistance stiffened, and Japan began incurring losses, this situation started to change, and while the straw that broke the camel's back for the Chinese might have been the Marco Polo Bridge Incident, for the Japanese it was arguably the Battle of Shanghai, which was initiated by the Chinese.

To answer your question, then, neither governments were particularly prepared for full-scale war leading into the 1937 Marco Polo Bridge Incident. But at the same time, as Japan was already engaged in a slow but steady expansion in China, it was only a matter of time before the Chinese either resigned themselves to defeat or began full-scale resistance. The Japanese did not plan for a total war against China because they were able to achieve their expansionist objectives without such a commitment and because they had other players to worry about. The outbreak of total war could, in this sense, be considered a blunder.

Even after the outbreak of full-scale hostilities in Shanghai, the Japanese government was still underestimating the Chinese will to fight. Government estimates for the war ranged from one to three months - that's the time Japan figured it would take China to capitulate. Their plans for the war and the occupation, therefore, should be viewed in the context of a significant miscalculation, as they simply did not expect the Chinese to put up much of a fight. As to what those plans were, you need only examine the occupation government they set up in Shanghai, Nanjing, and other provinces they conquered, which were staffed with Chinese collaborators, for the answer. That is, in the near term, they aimed to establish a puppet government in China, similar to what they had done in Manchukuo.

Sources:

S. C. M. Paine "The Japanese Empire: Grand Strategy from the Meiji Restoration to the Pacific War"

Marjorie Dryburgh "North China and Japanese Expansion 1933-1937: Regional Power and the National Interest"