Existentialism Curriculum.

The answer to the question might be more useful if you were to tell us at what level the participants of the group are and the extent of their philosophical background. I am sure that some time spent with Google, for example, might show several outlines from college courses that could be used if the group's Members had previous philosophical courses. There are also all sorts of introductory books covering "existentialism" many of which include selected readings.

I might have googled words I shouldn't have, but couldn't get much out of it.
The group of people have had a very basic reading philosophy, a few haven't.

A good internet place to begin is :
http://www.tameri.com/csw/exist/exist.html

Here are some introductory books to consider:

Walter Kaufmann, Existentialism from Dostoyevsky to Sartre, 1956
Paul S. MacDonald, The Existentialist Reader,2001

Both contain selected texts and introductions/commentaries.

William Barrett, Irrational Man:A Study in Existential Philosophy 1958.

Beginning with Nietzsche and Kierkegaard, the existentialist movement includes many of the most important Continental philosophers since 1900; it is important to remember that Existentialism is not a school of thought but a label that includes many different perspectives. One cannot read just a few texts and say to oneself, "Ah! so THAT is what it's all about."