Doing business in another state
I presume by "work" you mean service that your future LLC will provide to your clients in Missouri. If Missouri is the only state where your company would be operating then this is the state where it should be registered in.
Keep in mind, if you keep a home office in Illinois you would probably be required to register your LLC in both Missouri or Illinois (as domestic or foreign entity). In other words, I would need to know some more details about your future business in order to give a more accurate advise.