Inexpensive muslin or interfacing is what I would recommend. The "foundation pieced on paper" means that it was sewn to either a paper or fabric foundation. Very common in quilt to use up scraps. I like the rectangle look to this quilt. You might want to just draw a center line to guide you to get the same angle that the strips were sewn in the photo. Before deciding, make a test block first. If you use fabric, then you sew from the front. The fabric just gives the blocks stability especially with the bias edges.