Involving a professor somewhat is a good idea because it lends credibility and raises the importance of the project in the undergraduate's eyes. The student may find it much easier to disappoint or blow off a graduate student than to do the same for a faculty member. And the faculty member will be a better writer of recommendation letters. It's important to set a good example. Be honest in your dealings with people, in your measurements, and in your writing.
Publishing Use the same rules as for choosing the project.
If you have the student write, make it just a section or two, and then edit it afterward. I've sometimes had bad luck even getting my junior colleagues to read the papers their names are on. Thus, your primary goal should be to ensure frequent communication. Don't be a Dilbert manager. This makes it clearer what has really been accomplished and keeps everyone honest.