We've covered the first most important, which is the verb. The verb is the work horse of the story sentence.
The second most important part of speech or 'word' is the noun. The noun is nearly as important as the verb and runs a close second to the verb but it is not nearly the work horse that the verb is.
This is because the 'who 'and 'what' and 'where' are just as important as 'what happens' but it's the 'what happens' that carries the story.
With the "Who" the author can use the character's name, a pronoun, or even imply the character without using either because repeating the character's name over and over or even using too many "he"s or "she"s begins to draw the reader out of the story. The reader knows, or should know who the story is about from the beginning. After the "who" is established for the protagonist, the antagonist, and secondary characters, the most important thing is what they are doing or what is happening to them.
With the "What" or "Where" it is the same thing. Why is the "What" so important or the why "Where" even matters should be established more in the action involving them than in the author telling the reader why these things and places are so important. This is the difference between showing and telling.
So, bottom line... Nouns are important whether it covers characters, props, or settings. The reader does have to care about the characters and understand the importance of the things and places. Even so, the author must always remember that the verbs that carry the nouns through the story and not the other way around. This is true in all fiction and even more so in flash fiction.