It really depends. I know KD has a "list" of specialists that they hire for each season. They need plumbers, mechanics, electricians etc, etc. But "Wayne," the head of Maintainance, has worked there for a LONG time and has "earned" his position. That's one way of going about things. If you want to design coasters, I would think a structural engineer is the most fitting degree "route". In that case, you will most likely work for Intamin, B&M, GCI etc, etc... If you want to be on the "selection" committee for a specific theme park, I would think business management would be the best degree. You would most likely intern there for a while then move into the HR department, then general park management, then move up and up and up etc...
Oh and pretty much all those positions, will make you enough to live on your own
Hope that helps.