1-Double Lift
2-The Pass(Classic or Herman)
3-Breaks
Anything that you think surpasses these? Or that should be up there with them?
Eugene Burger doesn't use a double lift in his performances. The more you learn about card magic, the less important a double lift becomes. The pass is usually used o control a single card rather than its intended purpose of reversing a cut to maintain the order of a deck. Neither are fundamental.
The proper way to hold a break is fundamental, as is the proper way to hold a deck in dealers grip or overhand (Biddle) grip, to do a riffle shuffle or an overhand shuffle, etc.
Your statement is like saying, "the most important tools for building a house are a hammer, a radial arm saw and a pipe wrench." They are useful tools, but if that is all you have you won't be able to build a dog house.
As you progress in card magic, you will learn that the most important sleight is the one that fits best into an effect. Let me explain. You system know a cross cut force or a classic force but those forces are useless if you want to force an odd backed card. A Hindu force would work better, as would a riffle force with a double lift or Sankey's Witchata Slip. What if you have to force two cards? Similar with a control. A double undercut is great for a single card, but what if you have to control four cards? Then you need an Elias Multiple Shift or a variation (see Bannon's Smoke and Mirrors). What if you need to control a card to the bottom? Need a different control. Your list doesn't even address any false counts (Hamman, Jordan, Elmsley, etc.) or any palming techniques.
Ultimately, the most important parts of a magic effect are plot (what happens), method (the sleights used) and presentation (what you say to draw the audience into the effect, including principles of misdirection, patter, etc.). As you progress as a magician, you will be exposed to more plots, more methods and different presentations. You will become a better magician as you build a toolbox that has a variety of plots, a variety of methods and a variety of presentations.