Honestly just about everything sounds useful in some way, which shows how well put together the upgrade system is. I think that the only things that we could easily put off (but not reject entirely) are the Magic theory stuff (and even that might lead to actual useful spells, so maybe not) and the Performance skills.
For Violence we'll probably want basic skills in sword and shield to complete the knight loadout, at least one ranged weapon, and whatever else people want to dabble in before settling on a main weapon to focus on.
For Wistful everything other than Forge will increase our healing abilities to keep our teammates alive, while novice Forge might help us to at least maintain our armor and weapons once we get some.
For Lost increasing Stealth is generally useful, as is Barter and the Etiquettes. Don't think Lirra would like Larceny, but it might apply to opening locks in Dungeons?
Obsessed doesn't have many options, but they might branch into more knowledge trees, especially if Magical theory unlocks actual spells. Otherwise getting Lirra's literacy high enough for her to write properly is a good investment.
And of course, Faded echoes provide general knowledge, miscellaneous everyday skills, and our basic stats, so we'll always have something we want to spend them on. BTW
@Renu you mentioned including a Riding Skill earlier but I don't see it in the shop. Is it a Violent or Faded skill?