Lifelong Missourian. I have hunted from the Arkansas line to the Iowa line and from St. Louis to Kansas City where I live now.
Missouri is a great state in terms of public opportunities in either state owned/managed "Conservation Areas" or National Forest like the Mark Twain National Forest. You will not be alone. Our tags are cheaper than almost all bordering states such as Kansas, Illinois, Iowa, Nebraska, and Kentucky and they are all over the counter and not a lottery. We also have ~800,000 Firearms hunters a year for the November portion and it is the biggest outdoorsman event in the state, much like Michigan, Wisconsin, or Minnesota. Every hunter and their brother-in-law loads up an ATV and a pallet of Busch Light and heads to deer camp (which I honestly don't hate for the tradition and family time).
Archery season before rifle season is good. Scout ahead of time and commit to an area. There are good deer numbers on every CA state-wide. Camp near the area you are hunting. Watch every video from "The Hunting Public" on Youtube and you will have a great tactic crash course.
Another little known fact is that you can dive into the fray of gun season with archery equipment if you purchase a firearms tag. If you can find an Archery-Only Conservation area near other large blocks of public land that are open to general firearms, you have now found yourself hunting a refuge. Read the regulations carefully regarding hunter-orange, allowed-methods, etc if you try this. I usually move to my spots within city-limits or on the fringe to archery hunt during gun season as there is so much pressure, and this works almost every year.
It can also pay dividends to hunt any remaining food or food plots in the weeks after Christmas as deer become very concentrated on food sources.
PM me about your candidate areas once you have dates and regions narrowed down and I will give you some guidance.