you can certainly piece them for picnic quilts- the quilting part is dependant on your batting choice- has nothing to do with your pieced top-choose a poly batt (like dream poly) that lets you quilt up to 10" apart.
you can use anything you want for the back- more polyester- or cotton- either is fine- the difference is---cotton shrinks a little bit- polyester does not-
poly holds up like steel- washes and drys well- is good for utility quilts (ones that are abused--dragged around)
some people do not like using poly because it does not soften up like cotton does- it pretty much stays like it is---good for kids quilts- quilts that will take a beating-
the edges may fray a bit more than cotton (some times does- other times does not) if you have ones you find do fray- just use a little larger seam allowance.
have fun with them.