You can choose which stages you wish to attempt each day.
Items that can be earned as stage clear rewards vary by the stage.
[Character Development Stages] Heroics Textbooks, Maintenance Wrenches, Maintenance Drills
[Equipment Enhancement Stages] Utility Toolboxes for Each Equipment Slot
[Collection Enhancement Stages] Film of Memories, Memory Boards
Herostones can be used to increase your available attempts.