To add to Dallan's post, I believe the LE and CWMU draws take place first. These are generally the hardest tags to draw. If you strike out there (which most people do), you can fall back on the general season where you have to put in for a specific unit in the state and are confined to that unit during the general hunt. Even then, depending on which unit you choose, it may not be a sure thing to draw the tag you want.
Also, you can only put in for one LE species (deer, antelope, or elk), so if you put in for deer, it excludes you from the elk and antelope LE tags. You are also allowed one once-in-a-lifetime (OIAL) choice between rocky and desert sheep, moose, mtn goat and bison. If this interests you, pick one you like and stick to it. They are typically 15+ year tags, unless you get really, REALLY lucky.
Also, you can only put in for one LE species (deer, antelope, or elk), so if you put in for deer, it excludes you from the elk and antelope LE tags. You are also allowed one once-in-a-lifetime (OIAL) choice between rocky and desert sheep, moose, mtn goat and bison. If this interests you, pick one you like and stick to it. They are typically 15+ year tags, unless you get really, REALLY lucky.