As far as the students leading students thing, not all are like that. Granted that is how our program started out and how many still are, but some do have adult coaches. They don't get paid to do the position however. I believe that some schools are fortunate enough to have the game day coaches assist with club programs, but not all are like that. This year we actually have a former high school coach who runs her own business now in our area volunteer as our coach and we love her.
For the finances portion, as stated above we don't get anything really paid for us aside from gas money. We fundraise a lot and most comes out of our own pocket, which is why we try to minimize costs for everything. Instead of $10 hair bows, we do $1 ribbons. We pay for our own uniforms, which we keep, and the style of uniform is planned to stay for a long time. Shoes are up to the girl to buy if she needs them, as long as they are plain white cheer shoes. We don't have practice clothes aside from 3 t-shirts that are bought throughout the semester ($10-$15 each). Warm ups are totally optional, bags are optional, etc. though most people buy them.
Just something to think about would be to have a set plan for what the costs would be (the less the better for administration and the more likely they'll consider your idea), and a plan for how you would get people on the team, who would coach/run the team, where you would compete, etc. Also, does your university already have a traditional cheer team? You don't want to step on any toes there if they do, so make sure the competition team would be something different than what is already offered for the school (whether that be an intermediate team, STUNT team, team that competes vs game day)
