There is no one right sequence of words (I accomplished this mission on over 10 characters and only 2 or 3 times i dont have to buy more items.), but some words might works better then others in this mission.
Doing this mission i always using this template, and most of the time i dont need to buy many additional items.
Support of the Edron Academy
First try words: plea, bluff, flatter
Works best: flatter
Support of the Explorer Society
First try words: bluff, plea
Works best: bluff
Support of the Inventor Telas
First try words: reason, flatter
Works best: reason
Support of the Thaian King
First try words: all
Works best: flatter
Support of the wormtamer
First try words: flatter, threaten
Works best: 50% chance
Support of the Venorean traders
First try words: all
Works best: impress