I run several CP sites that provide and sell courses. I don’t use an LMS, not because it wasn’t possible, but because they all seemed so bloated and a pain to set up.
I think you should be asking what specifically you want to do, and then work out how to do it, rather than try to fit what you want to do into an LMS. If what you come up with is exactly what a current LMS provides, then use that. Otherwise, just build what you need for yourself. Most of what LMSs provide really aren’t anything special.
For example, are you talking one-off sales per course, or subscriptions? One big course or several smaller ones?
I didn’t know that you could make a course site without LMS in Wordpress/Classicpress.
Well, my goal is actually to create a site that has both free and paid crud. I wanted to be able to give certificate, offer quizzes in the courses and also offer videos in the courses.
Courses are really just categories, with each module a post within a category. Videos are inserted into posts as normal. You just need a way to stop non-students accessing the videos directly. (How to do this depends on whether you’re hosting the videos or not.)
Quizzes are a custom taxonomy, with each question a custom post type within the taxonomy. Or just use a specialist quiz plugin.
It sounds like your payments would all be one-off per course, so that just involves linking up with Stripe
I haven’t looked into certificates, but I doubt that’s hard to do.
Also, rather than using the default post (blog), you’d do well to create a custom post type (with categories) that isn’t hamstrung with default blog characteristics.