Assuming you bought from Midwest...they are the only coachmen dealer that i know of in STL...Def. need Sway control for this beast.Loading the camper is also very imp. to controling sway. I have found with a full tank, no problem....if i fill the WH (in back) it adds only 50lbs but does make a diff. The catalina line is rather heavy and tall compared to other trailers of same overall legnth and sway control should be manditory no matter what TV. JMO What state park are you talking about? A suggestion for your first time is to go to a site with full hookups to test everything....its nice to not have to worry about water levels and tanks durning this process. It lets you get fimilar with the valves and dumping the tank. It will also allow you to sanitize your fresh water tank while still using city water.
Get comfortable with the hitch....its the most important part of towing. I quit letting people stand around and watch during this process....very easy to overlook a pin or procedure.
Enjoy your new rig...MO state parks are hard to beat. A few new ones for us on the list this year. After looking aorund a little bit, there really are a lot of options within 2hours of STL. Hawn, Cuiver, Meramac, Mark Twain, Babler and thats not the COE's over in IL.