In regards to this particuluar question, I would say that they would probably be given a form for them to manage in. We would like it to be something canon (however it cannot be a computer or technological item) so that we can maintain some of the characters traits as well.

However, if the canon character does not have a form, I would say that they are provided a generic human body similar to what they look like in their world, and that form will change as they are shifting into their denizen.