which type(s) of "s"何時應有?

其實which types of 和 what types of 是錯的。
只有which type of 和 what type of 是對的。
以下是它們的用法。
For 'what type of', it means asking for a type, which is not classified carefully.
Eg.
Quincy: What is you favorite food?
Tarvile: It is chocolate.
For 'which type of' you have to classify carefully.
Eg.
Quincy: Which type of chocolate you like?
Tarvile: Dark chocolate...mm!
希望可以幫到你^^

“What type of” and “What types of”

使用 “What type of” 很普遍

What type of food do you like?
What type of dog do you get?
What type of house would you prefer to live in?

但是在特別情形下會用 ”What types of”
1) What types of jobs are available for the fresh graduates this year?
2) What types of fish are found in this lake?
3) What types of blood are compatible to each other?

所以用 types (plural) , 不用 type (singular) 因為期望的答案是 several types, 至少兩種類. 尤其第三問題, 涉及兩種類血 compatibility

I make up two examples to illustrate the point.

如果是靠工資為生的人 (wage-earner), 我會問
What type of car do you have right now?

如果是富豪, 又是汽車狂熱者, 猜測擁有兩三架不同類型的車, 我會這麼問
What types of cars do you have right now?

WHAT or WHICH?

In a question, the use of what or which affects the interpretation of the meaning. Which chooses from a limited range of alternatives; what is used in more general enquiries. Thus “Which film are you going to see?” suggests that the speaker has several possible films in mind; whereas “What film are you going to see?” shows that the speaker is unaware of the choice of the various films.
From another perspective, we use what when there is an indefinite (and often large) number of possible answers. We use which when there is a definite (and often small) number of possible answers.

What sports? Football, basketball, tennis, golf…
Which way? Right or left?

Hope that helps.

題外:
血種類 compatibility e.g. Kidney donor
• Donors with blood type A... can donate to recipients with blood types A and AB
• Donors with blood type B... can donate to recipients with blood types B and AB
• Donors with blood type AB... can donate to recipients with blood type AB only
• Donors with blood type O... can donate to recipients with blood types A, B, AB and O (O is the universal donor: donors with O blood are compatible with any other blood type)