it's an interesting question and one I struggled with when I started studying philosophy. For me the answer really does depend on the writer, and even on the work. For example Sartre's Being and Nothingness can be absurdly dense, but that is in part (at least I found) because it presupposes knowledge of Heidegger's work that proceeded it, whereas Existentialism and Humanism was written as a public lecture and is therefore much more accessible.
In my experience it is always better to engage with secondary sources where possible, particularly critical ones. This will allow you to build a more robust understanding of any theory and you can benefit from the work of all these philosophers and avoid 'going it alone'.
My method usually begins with a primary source, depending on whether I can make any sense of it with my current knowledge. If not I usually look for reader's guides, which can be really illuminating. Otherwise I will read through the source, making notes and summarising much as you do. I take notes, and after each chapter/section/paper I try to answer the following questions:
What assumptions are being made by the author in this text?
What is the main point/thesis of the text?
What are the authors objectives?
How is the text organised/structured?
How does the author support their argument?
Another thing to keep in mind is when you are reading, identify the parts that you think are clear and are not clear, try to discern what makes something more readable and understandable, and what obfuscates issues. This will set you in good stead for when you start your own academic writing.
Edit: I know that Sartre formed a lot of his views during the second world war. Before French occupation Sartre worked as a meteorologist for the French army. A leisurely job that involved sending up balloons and tracking their progress across the sky. He was then captured and held as a prisoner of war, during which time he is said to have first read Heidegger.
