Basics of sauce making are really based on the type of sauce your wanting to make. As the boss said Louisiana style is going to be peppers, vinegar and salt. When I make a new sauce based on a style, say Jamaica, I'll research what the staples of the place are. For my Jamaican sauce I use Golden Raisins, Pineapple, Sweet Potato, etc which are things typically used in Jamaican dishes but I also like to think outside of the box in alot of my sauce making and find those really odd things to try.
Were I to list what I believe to be staples typically used in hot sauces making I think I would list Onion, Garlic and Carrots as the trinity.
JMHO,
RM