Discourse is amazing software, but it is written with Ruby on Rails and the recommended setup (also used for this forum) uses Docker. It’s also needs various databases which are not provided by most web hosting providers. I don’t know if there is any web hosting provider in the world which could even support Discourse, but having a VPS for this is definitely the recommended method.
This forum was first built on Codoforum, then migrated to Vanilla and now running on Discourse. I don’t know how Codoforum is doing now, but at the time, it was quite buggy and incomplete software. Vanilla is not perfect either, but it was much better than Codoforum.
You may also want to check out Flarum. It’s currently still in beta and limited in features, but they share many design philosophies with Discourse.