Translation guide
This guide helps you ask 'what sort/kind of' in Japanese. The most common pattern is どんな (donna), but other options exist for formality and nuance.
The speaker wants to know the category, characteristics, or nature of something.
The most common and versatile way to ask 'what sort of N'. Casual and widely used in conversation.
どんな音楽が好きですか？
What sort of music do you like?
どんな本を読んでいますか？
What sort of book are you reading?
More formal than どんな. Often used in writing or polite speech.
どのようなご用件ですか？
What sort of business do you have?
Similar to どんな, but can imply asking for a definition or explanation. Slightly more emphatic.
どういう意味ですか？
What sort of meaning is that? / What do you mean?
Very formal and literary. Used in official documents or formal speeches.
いかなる理由があろうとも、遅刻は許されない。
No matter what sort of reason you have, tardiness is not permitted.
The speaker wants a subjective description or evaluation, often about experiences or people.
Again, the go-to pattern. Works for asking about impressions.
どんな人ですか？
What sort of person is he/she?
旅行はどんな感じでしたか？
What sort of feeling was the trip? / How was the trip?
Formal version for descriptions.
どのようなお仕事をされていますか？
What sort of work do you do?
どんな is the default casual choice. どのような is formal and often used in business or writing. どういう can ask for a definition or clarification, similar to 'what kind of (exactly)'.
どんな映画が好き？
What sort of movies do you like? (casual)
どのような映画がお好きですか？
What sort of movies do you like? (polite)
どういう映画が好き？
What sort of movies do you like? (asking for specifics)
While 種類 (shurui) means 'sort/kind', the phrase 何の種類 (nan no shurui) is not natural for general 'what sort' questions. It sounds like you are asking for a biological or categorical classification. Use どんな instead.
どんな食べ物が好きですか？
What sort of food do you like?
上司はどんな人ですか？
What sort of person is your boss?