Between North Korea, China, and Japan, which country would first take action against South Korea, and which would South Korea take action against?

The most likely outcome in the situation that you mention is that none of these countries will take any sort of military action against any of the others.  While it is true that South Korea and these countries all have conflicts of one sort or another, they are not the sorts of conflicts that generally lead to war.  The one exception that makes it hard to be certain about this statement is North Korea.  The North Koreans are something of a “loose cannon” and have already taken military action against South Korea on various occasions.  Even so, it seems unlikely that they will resort to full-scale military attacks on their neighbor.

There is a great deal of difference between countries “not liking” one another and them being willing to go to war.  To state the obvious, wars are bad for a country’s people and for its economy.  In the modern world, wars can be utterly devastating, particularly when they involve countries (like China and North Korea) that have nuclear weapons.  In addition, it is unlikely that any of these countries would actually gain anything worth getting if they went to war.  The US would not allow North Korea or China to conquer South Korea.  China would not allow South Korea to conquer North Korea.  There is no way that South Korea could take and hold any significant part of China.  In short, any war between any of these countries and South Korea would damage both countries without doing them much, if any, good.  Therefore, it is very unlikely that any of these countries and South Korea will end up in a war, regardless of whether they “like” one another.

The wild card here is the North Koreans.  They tend to act in ways that seem irrational and overly aggressive.  There is a chance that Kim Jong Un might decide that he needs to launch a major attack against South Korea.  It would not be logical for him to do so (from our perspective), but he might anyway.  North Korea has taken many provocative actions against South Korea over the years, including artillery attacks on South Korean territory and naval attacks on South Korean vessels.  However, it seems likely that even the North Koreans know that they can only go so far before they provoking a serious war that would harm their country.

Many countries have grievances against one another.   This does not, however, typically mean that they go to war.  I would be surprised if any of these countries took serious military action against South Korea and I would be shocked if South Korea voluntarily went to war with any of them.