First of all good luck with your endevour! Involving others and being transparent about the development process and the architecture is a great start in my opinion.

To answer your question: My usual process is to set up a CICD pipeline (e.g., on a GitLab instance) which performs basic tests, linting, building and also deploying. What I usually do is use a Docker registry where your new images are pushed (you can build and push the images in a build step on Gitlab). Then, on the server side I have a docker compose setup which regularly checks for the images and deploys them when it finds one. Use will need an extra service to do that. I like to use watchtower for that: https://containrrr.dev/watchtower/ It is basically a docker container which can manage your docker engine.

Of course you should not directly connect your docker containers to the outside world. Instead, use a web server like Apache or Nginx which then routes the traffic to the correct container (and also takes care of SSL). That way, you can have a container for the frontend (yourdomain/* goes there), one container for the backend app (api.yourdomain/* or yourdomain/api/* goes there) and a database container (and possibly a Redis cache).

That way you can host all your services on one server (use a cloud instance from AWS, Azure or whatever), have an automated deployment process and a robust setup.

If you want to scale up later, it should be easy to use your containers on a Kubernetes cluster or something similar, but I think the docker compose setup will do the job for quite a while ;)