I was in the exact same position, and I can't recommend Ruhlman's Twenty enough. It goes through 20 techniques/ingredients, from ‘Water’ and ‘Onions’ to ‘Roast’ and ‘Boil’, giving you all the information you might possibly need, and then provides a handful of recipes to explore all the avenues of each. The only downside is that a lot of the recipes include meat and the book never really touches on how to make sensible substitutes, which depending on your dietary preferences might be more or less of an oversight, but I didn't find it too difficult to sub things out.
I've not read Salt, Acid, Fire, Heat so I can't comment, but I assume it takes a similar approach.
Seconding Ruhlman's Twenty, it's the book that really taught me how to cook. By focusing on techniques, it allows you to understand that when a recipe says "saute onions on medium-high heat", it really means to sweat them, and what that looks like. So rather than mechanically doing what the recipe says, you understand how the ingredients respond to different treatments, and how to get the results you want based on your equipment. And when watching a cooking show, you can see what the ingredients are doing and understand why, so that you can fill in the inevitable gaps.
I've not read Salt, Acid, Fire, Heat so I can't comment, but I assume it takes a similar approach.