Having to look back and forth between the requirements of the quest and the dungeon select screen is a bit tedious, and frustrating if you misread the requirements.
What I ask is something like:
From the Tavern, clicking a quest will start the "choose adventure option" while "locking" the options that are valid to complete the quest. Any time there is only 1 option, it is skipped and automatically chosen.
For example, lets say a quest was Defeat Venture Cave, Southern Swamp, and Northern Deseret with the Wizard.
In this case, the Adventure screen will appear highlighting the uncompleted dungeons. After clicking, the kingdom screen will appear with the wizard class already chosen, waiting for a race to be selected. After race is selected, the player chooses dungeon preparations, and then hits Start Adventure.
If there is some requirement in the dungeon, a quest box will appear telling the player what they have left to do, and if they have failed any conditions. If there is still a requirement left after beating the boss, the retire button will warn the player that they still have stuff to accomplish.
Maybe you aren't doing your interface pass yet, in which case just keep this mind.