Fish Hunter,
Even though plugs (w/ single barbless) are technically legal, you'd better prepare for enemy fire if you fish that way on the Missouri. I've never seen anyone use anything other than flies and you will probably end up tarred and feathered by the locals.
Send an e-mail to Joe Bloomquist at the Missouri River Lodge (http://www.missouririverlodge.com) and he'll tell you what flies to use. If you REALLY want to get into the fish, hire Joe for one day to figure it out and then absolutely slay them from your own boat for the rest of your trip.
There are about 7,000 bows per river mile in the Missouri. If you really want browns, go to the Blackfoot.
Kevin