He had a choice. He could be either happy or angry with his life.
[This will be the answer to the questions below. Which question is suitable?
1. What choice did he have?
2. What options did he have?
3. What did he have to choose in the situation.
4. _____________?
Regardless of your answer, 1 and 2 are grammatically incorrect. "what" is a pronoun -- more correct would be "which" to modify the subject.
just a pet peeve of mine, like using "if" instead of "whether"
That said, #3 is not really a good question for that answer. One and two are okay, if you follow Steve's advice.
When asking questions, "what" is fine. It's one of the interrogative pronouns in English.
http://dictionary.cambridge.org/grammar/british-grammar/pronouns/questions-interrogative-pronouns-what-who
and
http://grammar.ccc.commnet.edu/grammar/pronouns1.htm#interrogative
Since the answer includes a singular (choice), I don't think question 2 is correct since it asks for choices.
Question 1 is fine; 3 is OK, too, but it's wordy.