As with all things web related there is lots of information available on the internet about the pros and cons of different image formats. In short, PNG and JPG (JPEG) are the most web friendly image formats.
JPG is probably the most popular choice for web images as the file sizes can be kept quite small requiring less download time. The tradeoff for small size though is image quality as images tend to be "lossy", meaning that information is lost when the images are saved which translates into lower quality images. JPG files also don't support transparency.
PNG is an image format specifically designed for the web. Unlike JPG it does not lose quality after compression and it does support transparency. If you want to keep the size small, but still retain the image quality, use PNG.
GIFs (which are not supported by Bitmaps) can be useful for small animations and do support transparency. Refer to 9.4 Storing Images (or Documents) as External Resources.