What is the best format to use to make clean looking thumbnails when they are enlarged on the web?
Thumbnails on the web are not the original image. Or at least they shouldn't be. You do not "enlarge" thumbnails to create full version images. You work the other way around.
Start with a large higher resolution image, then crop or resize to create the thumbnail image.
You should always work high quality to low quality, not the other way around.
Images will always be constrained to pixels per inch, so it is important to take into consideration screen sizes to screen resolution in determining how large your images will appear on various devices and the quality they will be displayed at.
- High definition: 600 pixels per inch (ppi)
Standard definition: 300ppi
Medium-Low res: 150ppi
Low res: 72ppi