Require exactly one category selected by admin?

I have done a ton of searching and there may be no way to do this, although it seems like there should be.

I am designing a site using WordPress as a CMS for my client. They are not web-savvy. There are a few different categories of posts they can use, but posts should not appear in multiple categories. I do *not* want to default them to a particular category if they do not select one, as this could easily be the wrong category for their particular post. I also do *not* want to have to create a separate user for each type of post — my client should be able to get in with just one login to manage everything.

So what I’m looking for ideally is:

-The ability to make category selection a radio button, and to require the user to select one if they do not make a selection but try to publish.

If that’s not possible, my second preferred alternative would be:

-Figuring out the URL I’d have to use to create an “Add New Post” link that pre-selects the category (something like “post-new.php?category=news”)

My last resort, I guess, would be taking out the add_meta_box for category and manually creating a post-new page for each category with the category selection made… but that seems way more hacky than I think would be necessary.

Any suggestions/help?