I have done it both ways. My first GFG quilt was running stitch and it was fine. I had to draw the 1/4 inch seam on the fabric so I would sew a straight line. ( I did 2 inch hexagons.) I am now doing the paper piecing with 1 inch pieces and it goes much faster - not easier, just faster. I have been doing an "I Spy" tumbling block using the plastic pieces. You can use the stick school glue with the paper to baste them, I have not tried it with the plastic, not sure it would work. (I am very new to the glue basting - wow! what a difference in time that makes.)
It is all a matter of choice - but I should add, that with the paper piecing you don't have the stretching that can happen without the paper. On the other hand, when you start with the whip stitches you can see them on the top. I don't think that is a big deal because they seem to disappear once the quilt it washed.