Relaxation and efficiency are the keys.
Muscle activity requires more oxygen and generates more CO2, so the less you have to do, the less gas you will use. You're right -- Being neutral starts it. Being horizontal is also important, because if you are tipped feet down, every kick will drive you toward the surface. To avoid ascending, you have to stay somewhat negative. Therefore, a lot of your effort is simply being applied to staying at the same depth, rather than propelling you forward. Achieving a horizontal position requires some adaptation in body posture, and also often some redistribution of weight, depending on where you are diving and how much lead you are carrying. Putting large amounts of weight in integrated pockets or on a belt often leads to an obligatory feet-down position. So does flexing at the hip joint -- Your body should be flat from the shoulders to the knees.
Sculling with the hands is often good information about buoyancy and balance issues. If you are pushing your hands down, you may be compensating for being negative. Similarly if you are pulling up, you may be too positive. Sculling repeatedly with one hand may indicate that your tank is off-center or you are otherwise unbalanced from side to side.
A good way to learn not to use the hands is to clasp them in front or under you. This is what NWGratefulDiver had me do when I was new, and it broke the habit pretty quickly.
Using an efficient kick helps reduce effort and gas consumption. Again, Bob taught me to try kicking just from my ankles, rather than a whole-leg flutter kick. This was surprisingly effective at moving me through the water at a leisurely pace that allowed looking around and enjoying what was down there to see. If you are in a flat, horizontal posture with the knees a little bent, you can scull with your ankles very easily.
Getting enough practice to where your buoyancy smooths out helps, too. In the beginning, if you are porpoising up and down, you are putting air in the BC and venting, and inhaling and exhaling to control your depth, which wastes a fair amount of gas. Once you polish this skill, you add gas on descent and vent it on ascent, and use your breath for fine changes (going over a coral head, for example) during the dive.
It's great that you are thinking about these things. The better you get at this diving thing, the more fun it is!