Docker Compose is simply a convenience wrapper around the docker command.
Everything you can do in docker compose, you can do plainly with running docker.
For example, these docker commands:
$ docker build -t temp .
$ docker run -i -p 3000:80 -v $PWD/public:/docroot/ temp
are similar to having this docker compose file:
version: '3'
services:
web:
build: .
image: temp
ports: ["3000:80"]
volumes:
- ./public:/docroot
and running:
$ docker-compose up web
Although docker compose advantages are most obvious when using multiple containers, it can also be used to start a single container.
My advice to you is: Start without docker compose, to understand how to build a simple image, and how to run it using the docker command line. When you feel comfortable with it, take a look at docker compose.
As for the best practice in regards to copying files to the container, or mounting them - the answer is both, and here is why:
When you are in development mode, you do not want to build the image on every code change. This is where the volume mount comes into play. However, your final docker image should contain your code so it can be deployed anywhere else. After all, this is why we use containers right? This is where the COPY comes into play.
Finally, remember that when you mount a volume to the container, it will "shadow" the contents of that folder in the container - this is how using both mount and COPY actually works as you expect it to work.
