The best place to begin is with your local landlords association. Most will have a sample lease that is consistent with Missouri law. Usually a month-to-month is referred to as a rental agreement, so that may be the term used for the document name.
The Missouri Apartment Association also has a lease.
Expect to pay a small fee.
Then adapt as needed to fit your particular situation - incorporating things consistent with your local law and ideas you get from this site.
I update my lease almost monthly.
--205.188.xxx.xx