A good way to reduce a web graphic is to use a program like Photoshop or Paint Shop Pro. The programs are equally useful, but they do have significant price differences. Both allow you to save an image as any file type, including the two that are the topic of discussion. It may take a couple of tries to get used to this but you will see big differences when you look at 5 different levels of the image. JPEGs are a little different.
Quality refers to the level of detail displayed in an image.
It's a good idea to try to create the best balance between quality and image size. Smoothing is a personal preference on how smooth the image should look. Smoothing can add neat effects to a picture, but does not impact the image file size or quality in any way. Once you compress the image and reduce the color levels there is no turning back. These are just some basic ideas to consider before beginning to design your webpages.