It's not really possible to make recommendations specific to Adapt... it all depends on your specific use-case.

For example, as with creating any graphic for the web, the best file type to use is going to be dependent on the type of image. Illustrative images generally work best as PNG or GIF; photographic ones as JPEG. Unless of course you're in the highly fortunate position of not having to support IE11 - in which case WebP might be the best format.

As Adapt is a responsive framework the width and height of articles aren't fixed. You might consider setting a different background image for each of the different screen sizes (by default these are: large - 900px; medium - 760px; small - 520px - but you can also set these yourself in the course config).