Best pictures for speed om web site

Stick to .png, .jpg or .gif file formats and keep the size of the images as small as possible.

That all depends on the goal and audience of the site.
If you are a photographer that wants to show his portfolio and perhaps sell his work, the required quality of the displayed images may be higher…

Regular images [illustrations of your text if you like] such as jpg and png will show adequately when stored at 72 dpi or slightly better say 100dpi and still do so at a good speed. The speed however may be greatly influenced by the available speed / bandwidth your webhost proviides, the number of images you display per page, other media displayed such as video, sound etc…

When displaying a large number of ‘big’ images, the available diskspace also comes into play.
Start with the recommended settings. Check the results and adapt accordingly.

The type of files used may usually only have a limited effect.
However… use png if you require a transparent background etc. Other formats such as jpg do NOT support transparency.

If you are a photographer that wants to show his portfolio and perhaps sell his work, the required quality of the displayed images may be higher…

The big mistake that many photographers make is trying to show all of their images (usually quite large) on their main posts page. This really slows the site down. I’d suggest instead that photographers stick to (thumbnail) galleries within Posts and allow visitors to select which images that wish to view at full size.