You are right, only "Какой спорт" is correct.
In general, "Что" in questions of such kind requires a dependent verb, which, however, could often be "is" (есть), which, as you know, is usually implicit in Russian.
Что полезного производит спорт? Что такое спорт? (= Что есть спорт?)
When you are asking to qualify or select one of a class, like in your example, you always need to use words какой or который. These two words approximately account for the subtle difference between what and which in your example: какой usually qualifies from a generic set of unspecified/unknown alternatives (какой цвет тебе больше нравится?), while который assumes a known set: который из этих цветов ты выберешь? However, какой is more generic and can usually be used for both cases.