What’s your favorite advanced weapon training and why?
My personal favorites are Versatile Training and Warrior Spirit.
With Versatile training, picking the Polearm weapon group can turn the Fighter into the face of the group, which I just find hilarious.
I love the Divine Bond ability for Paladins, so being able to do the same thing, but with even more weapon abilities available is fantastic.
My favorite is focused weapon which gives you war priest damage. It allows you do things like fight with sword canes or daggers and not be made fun of. I usually too many feats as a fighter so I usually pick up the extra advanced weapon training feat to get my focused weapons on other builds.
Fighters Tactics - Making teamwork feats work for you.
(I may or may not have an unhealthy fondness for teamwork feats)
Dazzling Intimidation - Dazzling Display is fun, but not practical as a full round action.
Armed Bravery - Not failing will saves is great
Warrior Spirit
Warrior Spirit, because it's the only magical ability a non-archetyped Fighter can get from the class. Non-magical classes simply make no sense in default Pathfinder.