Every task that shows up in the Adventure Journal must be completed. Make sure to check the Park Map for the '!', as talking to new characters is needed to activate their respective adventures. If you see other characters needing your attention, feel free to talk to them. Progress does not get reset for whatever adventure you are focused on and this saves some time in the longrun.
After completing a character's adventures, you get told to find more of their items. These are NOT required and will not show up in the journal. They are only needed if you actually want to get 100% for the in-game completion percentage.
Attraction tasks
These are tasks on attractions that a character has told you to go to in order to progress their adventure. Use this guide for specific chapters required to be played on the attractions and what you need to do:
https://www.xboxachievements.com/forum/showthread.php?t=3513...
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