How to punctuate an answer to a question when the answer is also a question?

Solution 1:

Sentences 2 and 3 are correct, albeit informal. You can fix sentence 1 by replacing the first comma with a colon, making it perfectly correct and formal:

Who should be baby-sitting your children: your neighborhood teenagers or professionally trained people?

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If you are curious as to why this is correct, simply replace the interrogative pronoun, who, with the noun of your choice. You should have the same correct punctuation:

Either of these/the following should be baby-sitting your children: your neighborhood teenagers or professionally trained people.

When in doubt as to how to punctuate a question, try to convert it to the non-interrogative form and punctuate accordingly. Questions are sentences in their own right, and thus should follow the same rules of punctuation as statements, except for the question mark at the end.