(Might be easier to argue for legalism, since it was more present in the Qing dynasty. But I’m basing the rest of my reply on your choice of Confucius)

So, a logical essay in that form would start by explaining the warring states period. Particularly focus on the troubles with maintaining power. Then, break down why each of the above ways of thinking was appealing to a ruler in dealing with those problems.

Now that we have a basis for the philosophies and context, you start making a direct argument. One paragraph, Daoism didn’t have staying power because [something about daoism and he warring States]. Another, legalism did not hang around because [argument about legalism and the warring states]. But Confucianism did stick around, [and here’s where you put why].

Since you want to come all the way to the modern era, make sure you do that for all three. “Daoism fell out of favor after the warring states, and today it’s mostly followed yada yada yada”.

Then for conclusion, follow the map one more time. Here was the warring states period, it inspired these philosophies for these reasons, but confucianism had the biggest impact because of blank.

Also, since I had to grade some similar papers as a TA, one last piece of advice. No using “Confucius say”. It’s not clever.