You going through all of the effort to get down to bare wood, I would stain and varnish. This is your only chance to do this and would be a shame not to take advantage.

Of course this depends on the door and if you want this look. Is the door cleaning up well? Is the wood nice to look at? Do you like stained and finished doors?

Only you know the answers. If in the future you decide that paint is better it isn't a major problem to prime and paint over the varnish.