They all will work well, I choose batting according to how I want the finished quilt to look. Poly for puffier quilts, cotton or cotton/poly for a flatter look.
Batting has different quilting requirements, so depending on how close or distant I want the quilting, I choose the batting accordingly.
Using fleece instead of batting, doesn't require any quilting, it is stable on it's own, the same with flannel, a wool blanket or other items that have been traditionally used in place of traditional batting.
Many of these were tied, but can be quilted too, just make a sample sandwich to see how you like hand quilting them, or how your machine likes them :D:D:D