To understand tone, you first must define what it means. Tone is the author's attitude toward his subject. You are right when you say many words could describe tone. Tone can be serious, scary, warning, sarcastic, humorous, teasing, and romantic. However, those are just a few examples.
Usually in a piece of writing, the tone is not directly stated. For example, you don't usually write, "The tone of this piece is ironic." Tone usually is implied. You infer the tone by analyzing how the author treats the subject. Is he poking fun? Is he deadly serious? Is he sarcastic?
I don't know what piece you are analyzing. However, the tone often is determined by the subject matter. For example, it would be in poor taste to have a whimsical tone when you are writing about an accidental death. However, whimsy might be just what you want when you are writing about some strange or funny event that posed no dangers.
Generally speaking, when you are writing a literary analysis, the tone is serious. You are trying to pull apart different literary elements and explain their meaning.