Kind of/ Type of ...

Hello!
I'm not sure about the articles that follow "kind of" and "type of" .

1. That painting is (a?) type of a modern painting.
2. It was (a?) kind of (a?) different story.
3. Her music is (a?) kind of (a?) piece of art.

To me the articles before "kind/type of" sound pretty odd.
Can you please explain how I should use the articles when I want to use "kind/type of" in a sentence?
I will be very glad, if somebody provide me some examples of those.
Thank you!