Six repositories as a single deployment Docker+CircleCI
With docker compose (or docker swarm if you want to distribute the containers) create a container for each Git repository. This should map well to docker’s philosophy of each container being used for a single purpose.

As far as examples go, I can recommend you have a look at veleda (shameless self-promotion) which combines 3 databases, a flask app, a ruby app (Grafana), Jekyll and nginx. It also includes unit tests that are integrated into Travis-ci and should be transferable to circle-ci.

Regarding the nginx aspect, 030 already mentioned that there are finished images to make your life easier. Even ones that include automated Let’s Encrypt services. 

Ansible can be integrated well into the mix. If you used it to install dependencies and network configurations, this is now handled by docker. For SSH-based tasks, ansible remains useful. Check out this comparison of tools and their scope’s of responsibility.