Which option did Qing leaders use to select government officials?

Legalism is the correct answer.

Explanation:

Legalism was the main school of thought during the Spring and Autumn period and Warring States period. The other schools were Confucianism, Buddhism and Taoism. Legalism was a political philosophy that considered the rule of law as a mean of organising society and as and ethical system. Legalises were against the Confucianism rule by virtue and were supported by the newly emerging middle class land owners. It was systematically formulated by Han Fei and served as the theoretical foundation for the highly centralised Qin dynasty.

Legalism was used I know this because I am from China