How do I create a Custom Course List?

I would like to create a custom course list. I would only like to display the course thumbnail image, course title, and the enrollment button for each available (published) course.

I would like for this list to have all new courses automatically added, similar to how the "archives" list displays all courses.

Is there a way to do this with short codes?

Also, can I get rid of the word "private" on the courses?