Another thing to check out - continuous line quilt patterns. That is the circles or waves you mentioned in your post.
Depending on the type of quilt square you create, you will want to stitch a pattern that helps/ softens/ embellishes the block you create. This pattern can be done by hand or by your sewing machine, whatever you have time and desire and energy to do.
Best of luck and keep us posted on what you do. We like to share our good and bad attempts as a big learning experience.