In Drupal 7, I can't find the Content types and Required setting under edit vocabulary.
How do I customise it?
Head over to the Manage fields tab of your content type. For example, for "article" that would be admin/structure/types/manage/article/fields. Then add a Term Reference field.
This question is about Drupal 7, but be aware that Term Reference appears to be deprecated and potentially be removed from Drupal 8 (in favor of the entity reference field). For more details on that, refer to the question about "Are there any benefits/caveats with using Entity Reference over Term Reference?", in which there is a comment also like "Term reference isn't going anywhere and there will be an upgrade path from 7 to 8".