I’ve actually already built pretty much exactly what you’ve describing 
(with a few other features as well). It’s currently a private plugin called “Discourse Learning Management”. This is what it looks like.
The plugin is covered in “unit tests” (i.e. it’s robust). It also has an “importer” system that allows you to import course content from remote sources.
The content you’re seeing in the screenshots is imported from here.
If you’re interested in using it / adapting it to your needs you can PM me and we can discuss what changes you might need and what kind of relationship we’d have.
To build this properly from scratch this budget is probably too low. You may get someone willing to attempt it for this budget however the end result may not be want you’re hoping for. To build just your feature-set from scratch (i.e. without some of the additional features we’ve added) my initial estimate would be a minimum of $5000 USD.
You’re also going to run into the issue of support and maintenance. Any LMS plugin for Discourse, no matter how “lightweight” will involve modifications which need to be maintained over time.