Nice clear straightforward question.
Good to see a question on this new feature.
Interestingly, there's an error on the BoL page: it says the CHOOSE function
Returns the data type with the highest precedence from the set of types passed to the function
The first argument is an integer, which has a higher type precedence than any character type, but if it really was going to return an int we would have string to int conversion errors here. BoL should instead say that the return type is highest precedence type of the arguments other than the first.