Some side stories focus on stat items, others on avatars. You can choose which you want to do based on what you'd like to focus on! It is not. STORY TIME. Maybe there is... Maybe not. Nope.
If we have to choose between two stories we should be able to see beforehand what the rewards are for each, doesn't make sense to not release that info. Impossible to actually know which one you want to go for.
No, that's a Challenge! Challenges are a separate thing from Side Stories and reward Party Medals, which you can collect to place on the Challenges Leaderboard. You do need to complete 1 Challenge in order to get your Story Token. You can then use this Story Token to choose your Side Story in the Store. You'll get a phone call once you've made some progress in the Main Story.