I recently received a whole load of quilts for Project Linus and many had fleece backings which of course the kiddiewinks love.
y personal preference is to use a thin wadding, one of my favourites is cotton "curtain interlining" sounds daft but it is super and cheap, a well known quilter told me about it.
One of the quilters had done a lovely job of the quilting, hers had trains on it, so what she did was to to and ordinary stitch around the trains, checking the back often and then FMQ stippling all over the background, I don't know if you can see it clear enough in this pic but it works a treat. By sewing around the trains first she "set" the fleece in place, if you can understand what I mean!