For my part I learned that the ratio was 15:1:)
I would disagree on runing rich on idle. If you do so, you may have a funy feeling while you apply full power on the runway.
In General Aviation aircrafts, here is what you do :
Lean the mixture on the ground to prevent spark plugs foolings. On take off at sea level, you usually don't take risks of a too lean mixture so you apply full rich. As you climb, you need to decrease the amount of fuel (lean) to compensate from the decrease in air density. (maintain 15:1).
If you start to ear "detonation" or his little brother "pre-ignition", you want to cool down your cylinders. One way to achive cooling is by allowing more fuel to "wet the cylinder", so you enrich your mixture.
In cruise, if you want best economy you pull the mixture and watch your CHT/EGT guage. As you lean it, the temperature will raise, then decrease again. Lean as necessary to be at "the peack" then enrich a little bith more to be "on the rich side".
For best power, you still want to find the "peack", but you will enrich till you loose 100 degree F... or 50 only, I don't recall.
If you don't have EGT or CHT guage, you can do it by ear by listening on the engine RPM.
Also, when you apply carburetor heat, because the air is warmer, it will be less dense thus you are runing slightly richer. On those small cessna, when you apply carburetor heat on the ground on engine check, you can ear/see the RPM droping from 1700 to about 1600.
Sorry that's all I know on the mixture use. I suggest you send an email to engine manufacturers like Continental or lycoming. They have ready to email documentations on how to operate their puppies.