How do you use 'types of things'?

There are so many sentences which can be constructed from the locutions you listed, that it is unreasonable to expect someone to ell you which one is "right," or which should be used in a particular instance. Without context, your question is unanswerable.

I'd be struggling to make a sentence out of 2 or 3.
I think you're headed up a blind alley.

Agree Mac, about 3, but 2 might be okay where things are arranged in groups

I think all of 'em, Jome. Even no. 3 might be okay in some context. "In what types of thing are you interested," asks my Better Half, whom most would agree is much smarter than me

In what types of concept is he interested
He's not interested in concept, but only types of thing

Okay it's a stretch