Which sentence is correct? Should I put "the" before "most"?
You must remember that the is a definite article. Quoting the explanation from Wikipedia,
A definite article indicates that its noun is a particular one (or ones) identifiable to the listener. It may be something that the speaker has already mentioned, or it may be something uniquely specified. The definite article in English, for both singular and plural nouns, is the.
The children know the fastest way home.
The sentence above refers to specific children and a specific way home; it contrasts with the much more general observation that:
Children know the fastest way home.
Which stage is most desirable?
Which stage is the most desirable?
When you ask me the first question, I do not have the concrete options to answer your question. But when you ask me the second question, we are already talking about stages and you are expecting an answer from a concrete set of options. I hope that I answered your question correctly. :)
"Most" without the definite article is an adjective meaning "very", but more emphatically, such that "it is not possible that you could be more welcome", e.g. "You are most welcome", or "it is most likely that it will rain before Friday".
"The most" refers to one choice out of a definite set of choices numbering more than two: "the most desirable solution is that which costs the least". For a set of precisely two specific choices, "the more" is used instead of "the most"; e.g. "of the wrists upon which one might expect to see a watch, the left is the more likely".
To address your explicit example, though, both forms are grammatically correct - they just ask different questions...
Three young ladies, all having been complimented with the expression "You are most charming", might playfully ask "which of us is most charming?" to which the best answer is "why, all three of you, of course!". No gentleman would dare to answer the question "which of us the THE most charming?" !
You are probably asking your students to select one and only one answer, in which case "the most" is correct.