Courses as Products - sort by class date

I am building a site in which the "products" are classes. We want to display the classes by the date scheduled in chronological order. I am using categories to group the classes by location to get site specific pages. Within each page i need the classes listed by date. I cannot see a good way to do this and need some guidance.

I thought of putting the written out date in the title but that becomes an alpha sort so does not work. I do not want to put the numerical date in the title. The classes are taught as a 3-class series by location so I thought of creating subcategories then sorting by title within the subcategory but do not know how to make that happen. Looks like the standard shortcodes do not sort by multilevel categories (or I do not know how to make that happen). This solution would work if there is no other way to sort by date. I would need help adding whatever code to the shortcode to make it work. I am not a programmer - I can hack code if guided but not write from scratch.

Any help appreciated.

Happy New Year!
Loretta