PUL is pricier than fleece, but nicer; fleece is perfectly sufficient.
I'd start out doing those three layers just top stitched, and if that works well you can try to sew it on the inside and flip it inside out. Since we're talking menstrual rags, however, that's really a bonus
---------- Post added at 03:41 PM ---------- Previous post was at 03:40 PM ----------
Oh, old towels are nice for the middle layer.