You can find most of the preliminary information per whatever unit(s) and whichever specie(s) you're considering, on the Department's website.
In relation to the "must have" species and the "must do" hunts, there's several literary publications (online publications and/or formatted publications) that you can subscribe to.
Also, since you're residing within the state, your own reconnaissance will tell you a lot about what you'd like to hunt and where you want to do it.
Maverick
1. The Spring hunt booklet is for mostly javelina, turkey and spring bear and bison hunts. (Usually out by beginning of October)
2. The Elk/Antelope period is called the "mid winter" draw because that's when the app period is. This is the most sought after draw period due to the quality of hunts offered. (Out by February)
3. The Fall hunt booklet for Just about everything else. This is where you'd apply for deer, bighorn, bison, fall turkey, etc..(out by June)
Hope this helps a little