That would have to be variables. How thick and type of plastic. There is a very stiff interfacing used to stiffen purses. Do know some use plastic canvas and cut and set in or make a pocket to put it in. I have used old notebooks my kids abandoned and they vary in texture and thickness. If you are able to stitch through it I would use an extra long stitch length. Will check back and see what the other cuties have used.
wow that sounds like a great question would love to see the basket!