Must-have, early in the game : Science (to travel quickly), Rhetoric & Imperial History (for not being ridiculous during the interview, much easier to have an advisor for Imperial History + boosting Rhetoric than having the other options), Etiquette, Empathy
Must-have later in the game : Repair + Visual + Invention (mostly for not being ridiculous with the Maus), some skills for avoiding assassination (mainly Condition and Body Control skills, eventually Layout, eventually Unarmed or Blade)
Very useful early in the game : Reflexes + Tumbling, Galactic Relations
Very useful later in the game : Piloting, Spirituality
Quite useful early in the game : Operations
Quite useful later in the game : Bureaucracy, Sports (if you want Ethexae to join), Musical, Dramatic
Meh : Media, Intrigue (just stays at 75 and don't care about it), Strength, Wrestling, Stealth skills, Economics
I quite never used : Gunnery skills, Environment skills, Demolition, Hunting, Military, Sleight-of-Hand, Chain
What I found more useful than expected is probably Science, Repair, and the Arts skills, to a lesser extent Spirituality.