General Info
In most cases, JPEG files work best for the web, in terms of finding a good compromise between image quality and size. After setting up and resizing your image or file in your photo editor, use the "Export to Web" option to save the image as a .jpg file. (You may also have the option to choose how much your file is compressed; a medium-high setting is probably best for most images. In Photoshop, which offers a scale of 1 to 100 for compression, a compression setting between 60 and 70 is recommended.)
There may be a few images on your site that "sit on top of" and overlay other images; in those scenarios, you will need to use a PNG file format, which is a special, high-quality image format that supports transparency.