I use Pellon fusible fleece but if you want it thicker go with two layers: one fused to the front and one to the back. It quilts up nicely either way and lays flat.

I'm going to follow this thread. I spent so much time making Christmas placemats and used fusible fleece, which I thought was thin enough. For me the placemats were too thick.

Run a few tests first.

Try Quilters Dream batting for machine quilting. It is 70% cotton and 30% polyester. It stays flat and does not crinkle up after laundering.

I used prewashed flannel. Not too thick and stays flat for glasses and stemware placed on it.