I made that jacket for my brother's girlfriend. We just used basic quilter's cotton from Hancock Fabrics. Lining is not required for that, but a facing on the front where it opens will give a nice look and like Railey98 said, finishing your seams will help a ton. I however, did line the whole jacket for my brother's girlfriend because she made all the gym badges and wanted them inside without the pin showing through the front. I had enough of the red and white to just line it in the same cotton that was the outside.
Here's my finished product: http://www.cosplay.com/gallery/210522/