Be aware that finely-shaded transparent GIFs may not turn out the way you want, particularly in instances where you've used a background color drastically different than the actual background color of the page the graphic lives on. There are others, but these are the most-used. The Joint Photographic Expert Group came up with JPEG some years ago, and it's become extremely popular. If you wanted a detailed discussion on how JPEG compression works, both for still images and motion video, click here . Be aware that the various compression levels of JPEG images affect image quality.
More compression equals lower quality but faster loading and smaller size.
A crappy image won't be appreciated by anybody no matter how fast it loads. While not conventionally a graphics format, the Adobe Portable Document Format exists and is widely used. I have some strong opinions on the use abuse of PDF, though. PDF files are literal graphic renderings of formatted pages of text. Their most common use is to provide online, viewable and downloadable documentation.