I prefer 100% cotton for batting. Like the way it "crinkles" when washed, and it gets softer with every washing. Also like the way my machine stitches get hidden; polyester batting has more loft and doesn't shrink, so it seems as if my mistakes show up a lot more.
In terms of fabric, you can use almost anything to make a quilt. However, poly is more slippery than cotton, which makes it harder to match seams accurately. Poly does not crease like cotton, so is also more difficult to use for turned applique. Poly also frays more than cotton. It's usually not a good idea to mix poly and cotton in the same quilt as they fade differently; poly doesn't fade at all, while cotton "mellows" with exposure to light.