Categorizing content types
You can't add fields to the content type in regular old Drupal.

Also, the thing is that the view itself is pulling fields from the actual entities you're trying to list, so even if you manage to somehow add tags/fields that relate to the content type (through a custom or contrib module), your views wouldn't be able to just access those special fields by default.  After all, your views are actually pulling entities themselves and accessing their fields.  You know?

The simplest way to do this, I think, is to hard-code which content types you want listed in your views as filters:

In your views' 'Filter Criteria' section, simply add the filter 'Content: Type' and select all the content types to include.  So, if you wanted a view that applies to 'news' category types, just filter to include all those content types (news, image news, etc).  Of course, if you ever add a new content type or want to change your categorization, you'd have to edit your views by hand to match the new way of doing things...

The above is better, in my opinion, then adding a 'content category' vocabulary that is included in each of your content types as a field.  Even if a 'category' vocabulary has a default, which allows content editors to create nodes and not have to set a category, the problem is that tagging each node (versus filtering by the content types as above), would make 'switching' your categories or removing/adding categories to your content types harder.  If you decide to change them later, what do you do about all the nodes you've created in the meantime that have been tagged a certain way already?  :-)