If you are unsure of what programs the receiver has save as an EPS file. These files need a graphics program to be able to open. We like these for photographic images as we use Adobe Photoshop. You could also save as EPS file or tiff to share with others. A very common format that cuts down on size as it doesn't include all the formatting found in say a Photoshop file.
Bitmap images contain no grey areas.
A lossy compression format best left for simple images on your website. JPEG- Another lossy compression format. We use this a lot for photographic images. We find this as an excellent way of making large files small without changing the quality. Used by PC users.