Indefinite article "a" before a countable noun following "a kind of"

Hi. Please help. When do you put the indefinite article "a" before a countable following the phrase "a kind of," "any kind of" or "some kind of"? Thank you in advance.

eg,
1. To him, looking for any kind of a manifestation is a foolish thing (to do? - should I put this part?).
2. To him, looking for any kind of manifestation is a foolish thing (to do - should I put this part?).
3. He wonders what kind of a person would talk bad at such a person.
4. He wonders what kind of person would talk bad at such a person.