Waifus are still serious business I see. Anyway, I think I'll try playing with a short party of 4, for some reason I always preferred smaller parties. I'll put all good aligned characters as core and then ad the rest when dealing with their crap quests. It's going to be an all out magical party. My character will be a gish of some sort, Octavia is an obvious arcane trickster, Tristian is a cleric/sorcerer/mystic theurge. But what about Linzi? Can she do better than a plain boring bard?
Straight Bard is probably the way to go, aye. Inspire Courage is valuable. You could mix in 1 level of Fighter, go 7 levels of Bard, and then prestige her into Eldritch Knight if you want, but she will lose inspire courage progression and 2 levels of spell progression, so I wouldn't really call that an upgrade, esp. since Inspire Courage boosts your party's attack and damage.
You should probably build Linzi's feats and gear as an archer. Give her Point Blank Shot, Precise Shot, Deadly Aim, Rapid Shot, Arcane Strike, Manyshot, Clustered Shots, Hammer the Gap. Then again, that might be a waste if you just want to use her as a pure spellcaster in combat. But Linzi's weak charisma means she might be better off avoiding any spells that depend on saving throws.
Woah, woah, woah, woah, woah. Hold on.
Alchemists in PF:K qualifies as arcane casters, and their extracts as arcane spells? That has... potential, especially if they introduce more PrC:s later.
No. Vivisectionist Alchemist has sneak attack. He replaces the Rogue level (add in Accomplished Sneak Attacker), you take 3 Wizard levels, and you progress spellcasting as a Wizard through AT, but you still have the perks of a 1st level Alchemist instead of a 1st-level Rogue. Unless you need trapfinding, 1 level of Alch is much better than 1 level of Rogue.
If you want to fuck around as an Alchemist, dip one level of Fighter or Barbarian and go play as a more armored brawler Alchemist, since they have no arcane spell failure. Barb 1 + Alch 1 is 28 str at level 2, but you'll need to keep up rage rounds.