Which image format should I choose?

The image formats used on web sites are JPEG (or JPG), PNG and GIF. JPEG is best for images with many colors such as photos. GIF is best for line art, illustrations and drawings with limited color. PNG is the most versatile and can be used quite broadly on web-sites.
The image formats used in documents follow a similar rule. GIF, TIFF and PNG are best for images with fewer colors and JPEG is used for images with many colors such as photos. The best test is to use pdf2image to convert to a few different formats and then view them both on-screen and in print to see which gives you the desired result.
It’s also important to determine what formats your application can import. If the program you want to use only accepts BMP, then you need to convert to this format, even if it produces larger files than PNG.