One thing I am a bit fuzzy on and this may just be me missing something in the rules but can you use your skill improvements on your weapon skill or armor skills?
So can you burn one of those skill improvements to move something from trained to expert or is the only way for weapon/armor skills to improve is via class based specificly listed improvements?
I think it is the later but there is some argument in my group on that and they say the stated class ones are just bonus improvements if you did not already spend an upgrade on it.
You have a weapon proficiency and armor proficiencies, but there is no such thing as "weapon skill" or "armor skill," so no you can't use skill boosts on them. Can't use them on your spellcasting proficiency either.
Okay so that is kinda what I thought only improve those when stated specifically by the class/feat. That does seem like it is going to get kinda tough on people like alchemists who can't sustain their special attacks for all combats and never get particularly good with weapons either.
It's possible to gain trained proficiency in all armor, simple weapons, and martial weapons with the Fighter Dedication feat.
At 12th level, the same character can gain expert proficiency in a weapon group with the Weapon Expert feat.
I haven't seen a way to increase armor proficiency, yet. However, shield use can be picked up and improved:
Any character that is trained in light armor can take the Shield Proficiency general feat.
A character that is trained in shield use and has already taken the Fighter Dedication feat can take the Basic Maneuver feat to gain the Reactive Shield and/or Aggressive Shield fighter feats. On reaching 12th level, they can take the Advanced Maneuver feat to gain the Shielded Stride fighter feat.