The files I supply are PDF and PNG because these files are the best of all worlds.
The .pdf files are the perfect files for printing and do everything that an .eps does (.eps is the traditional professional print file) and it has a vector edge. This means you can make these files as big as you'd like and no pixelation will happen, it also has a transparent background. The best file to use for digital (website, social media etc) is a .png. These do everything that a .jpg does, but they have the added bonus of having a clear background meaning you can use these on top of colour and never worry about an ugly white box.