GIFs are usually only best for images where there are large flat areas of a single colour, such as a diagram. Gifs can have transparent areas in them, and can be animated, which a jpeg can’t. Gifs are also limited to 256 colours.
JPG/Jpegs are preferrable to gifs for almost any image that isn’t a diagram. Jpegs compress the data very well, meaning that your picture files will be smaller. This compression creates inaccuracies though, but these inaccuracies are not usually noticeable. In Photoshop, always set your picture quality to 60. This gives almost no visible quality loss, and it halves the file size. Don’t be tempted to try to reduce the quality. It’s very hard to judge.
PNG are Short for Portable Network Graphics, the third graphics standard supported by the Web ( though not supported by all broswers ). PNG was developed as a patent-free answer to the GIF format but is also an improvement on the GIF technique. An image in a lossless PNG file can be 5%-25% more compressed than a GIF file of the same image. PNG builds on the idea of transparency in GIF images and allows the control of the degree of transparency, known as opacity. Saving, restoring and re-saving a PNG image will not degrade its quality. PNG does not support animation like GIF does.