I have done all of mine on paper. I have seen pictures of them done without foundation--but I'd worry about stretching. If you use muslin, it won't be removed, so that takes away one step vs. paper. The quilt would have an extra layer of fabric, so I assume it would be warmer.
Something to watch for: if you use a single color in the center of each block to create a pattern, position it carefully and consistently, so it will line up across blocks. String blocks are very forgiving since they don't have to match along the sides, but the center strip is important if you want to create a pattern across the quilt.
Have fun--these are my favorite blocks to make!
