Update, January 2019: I would like to point out that using Drupal VM to build production servers is not officially supported, and though it may work pretty well, you are own your own if you do use it in that capacity. Please see Drop 'official-ish' support for using Drupal VM to run production servers for more details. What follows was mostly a tech demo for a MidCamp session, and has only been used by a small fraction of the Drupal VM userbase.
In preparing for my session Developing for Drupal 8 with Drupal VM at MidCamp later this month, I wanted to build out an example of a canonical "this is the way I'd do it" Drupal 8 site using nothing but Drupal VM and Composer. And I wanted to build both my local development environment and a production environment on DigitalOcean, all using the Ansible automation playbooks built into Drupal VM.