This mission has different rewards for each character you choose. For Irene, Sion, Ray, and Anne, you will get unique masteries. I would advise finishing all the routes. Same for the next mission.
Right away? Are those masteries that valuable? Also replay them via story mode thingie in your office?
Yes, you need to replay them from the office ('case records'). The masteries you get from Sion and Ray routes are essential. They let you have extra TP (ray) and convert basic slot to attack or defense (sion). Same for the next mission: all three routes will give you masteries that are needed for build tetris.
Any more story missions that warrant repeated playthroughs?
-First fight Heixing vs Carter(3.5). If you win you will get 'Breakthrough'
-Scent of the Past (park mission): Irene, Sion, Anne, Ray routes give masteries
-The next mission (police training): all three options give masteries.
Now, I need to be cryptic to not spoil stuff for you.
-In a cold mission, where you need to rescue someone from beasts, you have an option to fix something or run away. Fixing raises your self-esteem, running away gives you mastery.
-In a train mission that involves a bottle of wine, both routes give masteries.
-In a mission where naked man duels in the ruins, if you win you will get a mastery.
Hope, I did not spoil you anything)