I've made about a dozen now and have experimented a little along the way. I use pellon on one and a heavy duty fusible interfacing on the other. Depends on the look I want after quilting to which side I apply what.
The number on the pellon here is 640 which seems to be the thickest. I used it in both the inside & outside for my first couple of bags but didn't find it too thick to sew through. I recently used Matilda's 100% cotton batting in one as it was ordered in specific colors and I thought it needed a little heavier lining.
My original reason for experimenting was due to cost. Pellon $15.95 per meter.