Unfortunately, JPEG uses a lossy compression, meaning that once you save it as a JPEG and lose the original image, it stays as a crappy image. This is the main reason why you wouldn't want to save images as JPEGs, and the rate of quality deterioration depends on the algorithm being used, and what the image originally looked like. However, the image size savings are very good, and JPEGs work the best on images that don't have sharp contrasts. All I can suggest with JPEGs is to use what the above user suggested, and just see what it turns out looking like.
The alternative is to save the image as a GIF, since that's the other image type that can be used for medal icons. GIFs use lossless compression, meaning the original image can be restored. However, in my experience GIFs tend to sabotage the quality a little bit if there's a large range of colors that need to be displayed. Again, just try and see how the image turns out if you're worried about quality.
fyi, if you repeatedly save a JPEG in a JPEG in a JPEG etc., the image becomes super craptastic!