But in order to do so, we need information from Commons, and we want to make this as easy on the WMF servers as possible, so we'd appreciate some help and pointers. What we're looking at retrieving is information about (1) title, (2) author, (3) license, and (4) thumbnails of medium size.

From what we can understand, you can request any size thumbnail on an image simply by prefixing it with the size you want (like 123x-Filename.jpg). But it seems really silly to always request 640x for instance, since that would mean the WMF servers would need to generate that for us specifically if the resolution doesn't exist.

What we'd find much more appealing is to be able to determine before making the call what sizes already exist and which can be retrieved without the WMF servers needing to rescale them for us. And while the viewer on Commons do seem to offer thumbnails in various sizes, we can't seem to get that information from any API.