Often if you use an online travel agency (I personally use Orbitz, others like Expedia and Travelocity may or may not do the same thing) you will find that they search and find precisely these kinds of fares. If you have them book it, you will get a single ticket issued on the paper of the first carrier you are traveling on. This will allow you to check your bags through, and in case of irregular operations like a late arrival you should be allowed to rebook; you will not be treated as a "no-show." Your baggage allowance, if any, would be that of the first carrier you travel on.

Whether you have to re-enter security will depend on the layout of the connecting airport. I have not flown through STL in many years. If the gates are in separate terminals, you might have to exit one terminal and re-enter through security in another. For example, in Atlanta, you can go from terminal to terminal freely, but in Boston, some of the terminals are separate and you have to go outside and come back in.

Orbitz sometimes charges an extra fee for tickets on multiple airlines, but it's probably worth it to get a single ticket like that. The fee will only be in the $6-$10 range.