どんな どういう どのような どういった It is all same meaning Nuance is slightly different each. どんな＜ {どのような、どういう、どういった　same polite image than どんな｝

どんな is good. No の after it, so どんな映画(が好きですか)？ Answers would be "stupid movies" "light-hearted movies" "horro movies" どういう映画 would work as well. Answers would be "movies that make you think" or "movies that are very slow-paced" for example. どのような would be asking about technical things regarding the movies. I'm not sure I have a good example for this one in this context, but the answer to that question could be something like "movies filmed in 16mm with a Nikon camera" or "movies that exhibit the touch of Peruvian directors during the late fifties". It's like asking about the movie as a thing, not about the movie for its contents.

Try どういう映画が好みですか？