There is no objective way to determine which of these factors was the most important in bringing about the start of World War I. All of the factors had an impact and it is not possible to accurately measure each of these impacts. I would argue that the most important overall factor was the desire for empire and power. This desire caused alliances to form. Once the alliances were formed and the various countries were completely suspicious of one another, the assassination could ignite the powder keg and cause the war to begin.
The most important of the factors that you mention was the desire for empire. However, it was not just the desire for empire but the overall desire for power that caused the war to begin. Countries wanted empire because empire was a means to achieving economic and military power. They also wanted empire because possessing an empire gave them greater prestige in the world. Because they wanted these things, they competed with one another. Their competition included such things as the arms race and various provocative actions such as the German attempt to stir up trouble between the people of Morocco and the French in 1905 (First Moroccan Crisis). As the countries competed, they came to distrust one another more and more. This was the real cause of the war.
As the distrust between the countries grew, they formed alliances with one another. They felt the need for alliances so that they could have friends who would help to protect them from threatening opponents. For example, France and England (who had been rivals) formed an alliance because both of them felt that Germany was a threat to their power. Thus, the alliances came about because of the desire for power and empire.
Once the alliances were set, all it took to start the war was a relatively small spark. This is where the assassination came in. It caused Austria to want to go to war with Serbia. When this happened, the two countries’ alliance partners jumped in and made the war spread rapidly until it became a “world war.”
From this, we can see that the desire for power and empire was the most fundamental of the factors that you mention. The desire for power and empire helped cause the arms race to occur and alliances to form. Once these things happened, war became much more likely and the assassination was a sufficient spark to set that war off. The desire for empire and power is the most important factor that you mention because it caused the other factors to occur.