Most global maps don't preserve areas anyway, and the only projection that is equal area and fits exactly into a rectangle is Cylindrical Equal Area.
"Apparently the proper way to do this is to work with random numbers, like 1:10000000" Uh, randomness does not enter into it, and a number by itself is not random, it's the process that produced it that is, not that 1/10000000 is a number most people would think of as being "random" anyway or that randomness would be in any way relevant to scaling maps.
"but I need the scale to be the exact size of earth" This makes absolutely no sense. I have no clue what you are trying to accomplish. If you hadn't already said the planet is larger than Earth, I'd assume you meant they need to be the same size but as it is, I have no clue.
I'm sorry but if you have a clear idea of what you want, you aren't expressing it effectively.