Reversible garment using quilting cotton and fleece

I am making the lullaby layette jacket, which is reversible, with quilting cotton on one side and fleece on the other. I expect the cotton to generally be worn on the outside. I am seeking some general guidance on what stitch to use when joining seams, stretch or straight? Would a quilting needle or ball point for my machine work best? I would lastly like guidance regarding the sleeves. Am I better off sticking with fleece for the sleeves or should I go with a woven cotton for ease here? Any other suggestions for using these two fabrics together is appreciated as the general guidelines for each are definitely different. Thank you!