There's really only one equation necessary: that of determining the cost to level a character to the minimum required by a story mission.
The best way that I've found (at about 2030 while watching Chuck) is this equation, where c is the cost to get from level 1 to level x+1, and s is the cost of a "step" (the slope in the linear equation that governs cost per level):
This is an interesting case of the triangular numbers, and an implementation will run in constant time (as opposed to the naive method of summing with a fold or loop). At some point I'll write a proof, but today is not that day.
The equation used to determine the materials used to get to level x to level x + 1 is: