I want to be able to upload files and either immediately or after upload assign multiple categories to them. I have 3 different kinds of PDF document: Treasurer report, minutes, and newsletter. What I want to be able to do is have a user assign a document type prior to the upload and have that type translate into multiple category assignments per document kind, like this:

Treasurer: Assign Categories A, B and upload file to media library Minutes: Assign Categories, C, D and upload file to media library Newsletter: Assign Categories, E, F and upload file to media library

I am aware of wp_handle_upload but have been unable to find anything showing how to use it so set the category at the time it uploads. Is that possible or is there a better way?