What is the best free way to publish my site?

Assuming you want to do the work yourself and not use a site builder, Neocities, GitLab Pages, or GitHub Pages are good choices. With Neocities, though, I believe you need to have a paid account to use a custom domain.

More options :

https://neocities.org

https://app.netlify.com/drop

GitHub for one has rules about monetisation, is that an issue?

Gitlab/Github pages?

Vercel