If you are unsure about what KC barbecue is suppose to taste like, than you need to go to Arthur Bryant's. If this is your first time going to an Arthur Bryant's, you must go to the one in downtown KCMO. They have a location in KCK which is good and tastes the same, but not the same atmosphere as the original. This place has the best BBQ in the country (IMHO).
One of the must-haves is the burnt-end sandwiches. The sauce is the best in the city.
Make sure that your not in a hurry and you can savor the smoked meats. Also if your in a hurry you will undoubtedly get your clothes all messy due to the sauce.