Consider the following:
1. What type of person are you looking for?
2. What types of person are you looking for?
3. What types of persons are you looking for?
4. What type of persons are you looking for?
In informal English, the word after the "of" is often plural. But in the most elegant formal style (university-level papers, etc.), the noun after the "of" is always singular; it is the word "type" (or "kind", "sort", etc.) that is singular or plural (choices 1 and 2).
In informal English sentence 3 is often used. Note that it has a "double plural": both "types" and "persons".
Sentence 4 is used less often than sentence 1, in my experience.