For the photograph you could use JPEG or JPG format. This format is better suited to images with lots of colours and smooth textures.
For both the cartoon and the pie chart you could use GIF. This is better for images with limited colours or large areas of flat colour.
The basic rule is:
Lots of colours -use JPEG. For solid colours or no gradations -use GIF
Note that there are other image file formats such as SVG and PNG which are not as widely used.