Which of the guided projects through the course are relevant to include in a new portfolio for a prospective company?
Project 1 at the end of the first mission guides you to work in the Juypter notebook within the module. Should I instead be working out of my Jupyter notebook on my own computer to start building my portfolio?
Finally, is it important at this stage to push notebooks to GitHub?
Except for the jupyter notebook intro project, all of them can be included in your portfolio. I would recommend you to update each of your projects with the new knowledge you will attain as you progress through the path.
Pushing notebooks to GitHub will enable you to easily share your projects because GitHub can render the .ipynb file. It is also useful to avoid situations like this: