There was some more conventional fighting between the Nationalist and Japanese forces, especially early on, but for the most part the Nationalists were very much outgunned. China had been working to modernize its army with German help before war broke out, and as a result was building the core of its army around units designed around the German model. Unfortunately for China, while these German-trained soldiers performed very well, they lacked adequate support from critical elements like artillery and aircraft. The bulk of these elite forces were thrown into battle at Shanghai in the beginning of the war, and they were mostly annihilated during that campaign and the following retreat. Outside of those elite forces, the Chinese army struggled from general poor organization due to the large mixture of equipment they had on hand the their poor industrial capacity, especially once they had been pushed out of the coastal cities.
Outside of the early waves of conventional warfare, the war largely stagnated into a guerrilla war - the Japanese were already overextended administering what they had conquered and struggled to go much further, but the Chinese lacked the ability to make any significant gains, being repulsed every time they made an attempt to do so.
As far as weapons, there were areas of nominal parity between the forces, but for the most part Japan came out on top. Japanese infantry weapons at the outbreak of war were
Later on, following experience in China showing that their 6.5mm rifle round was underpowered, the Japanese would move to adopt the 7.7mm round of the Type 92 as an infantry rifle cartridge, producing the Type 99 rifle and light machinegun. However, due to the supply strain, 7.7mm-chambered weapons would never fully replace the older weapons in Japanese service.
China, on the other hand, had a large mixture of weapons both procured abroad and built domestically under license. More famously, they were enthusiastic users of the Mauser C-96 "Broomhandle," setting up extensive domestic production and developing several variants, including versions with 20-round magazines and automatic fire capabilities, as well as a variant chambered in .45 ACP (as opposed to 7.63 Mauser or 9mm). Mauser 98s from both Germany and Czechoslovakia were also common, and some domestic production of the Czech versions was done. WW1-era MG08 heavy machineguns would be produced domestically in large numbers by China, and large numbers of ZB.26 and vz.30 light machineguns would be imported from Czechoslovakia and produced under license. German support early on also provided the Chinese with a variety of German-built submachineguns - oddly enough, one of the few areas where the Chinese did have a significant advantage over Japan. Given the guerrilla nature of the war, particularly in the northwest, captured Japanese weapons became common in Chinese hands as well. The Soviets would provide some more active support for the Chinese later on in their war that was most clearly seen in the presence of Soviet fighter aircraft, but some small arms were provided as well. More prevalent was the large amount of American and British equipment that would flood into the country under Lend-Lease once the Americans were pulled into the war.
The wide variety of equipment listed doesn't really get across how poorly equipped China was, however. Infantry weapons are one thing, but China more critically was lacking in support weapons - aircraft, artillery, and antiaircraft guns. The Chinese Air Force was rarely able to contest the skies, and in critical moments like the Shanghai campaign, they were completely powerless as the Japanese Army and Navy air forces proved devastatingly effective against Chinese ground troops. China would receive some modern fighters in the form of Soviet I-15s and I-16s following the fall of Wuhan, but poor training and supply and low numbers available would prevent them from effectively contesting the skies over Chongqing, deep in the mountains of the west. Artillery and antiaircraft guns were scarce, poorly supplied, and poorly trained.
Perhaps the best demonstration of how poorly equipped China was during the first few years of the war is the Battle of Khalkhin Gol - the last Russo-Japanese border conflict. Japan resorted to things that seem absolutely suicidal in retrospect but had served them perfectly well so far in China - ancient artillery pieces guided via a spotter in a balloon, slow-moving light bombers with a handful of 15 and 30 kg bombs, infamously poorly designed tanks, and a general lack of mechanization that would ensure that they suffered from constant supply problems. All these practices had served Japan excellently in China thus far, but even a Red Army beset by purges and operating in some remote theater several days from the nearest railhead was able to nearly annihilate the Japanese forces present.