What I'm going to say is simple:
While there are teams that can be successfully student-run (see Libby's post), they are the exception, rather than the rule.
What's going to happen when Libby graduates at the end of this year? It's almost certain that her team will continue, if they have someone to take charge. But if nobody steps up, then the team will fold. And many high school students wait for somebody else to step up.
You almost have to have an adult who can continue the team while student leadership transfers over. The adult is not necessarily a team leader; rather, they are the last in the line of succession, but have to know the most in case the entire line goes down. Or you can do like merybar's team is doing: rotating coaches. One runs the team, but has to step down, so a student steps up and runs the team until a new coach arrives.
Your situation, as best as I can understand it, is: Your adviser is stepping down after three years. Your team is for some reason changing schools. (I don't know how that works, but please don't post it in this thread. If it's something important for us to know, PMs or FAHA is probably better, or I miss my guess.) You want to start a new (rookie) team at the new school. Your current team has one sponsor (who you evidently don't care for). Am I correct so far?
First, if at least 5 students are going with, you're not a rookie. That's how FIRST chooses to define it. So you may as well keep your current number if you can, even if you do transfer over.
Second, you really want at least one adult. I'm not talking one fresh out of high school, I'm talking one that's a little older and more mature. Said adult would,
under this system, mainly be the accountant/order keeper, in effect.
Third, why on earth do you want to start completely from scratch? That's not a good idea! I was talking with another FIRSTer today over lunch about logistics of starting a team. You're talking fundraising at least $10K, per year. And you only have students doing that? If I'm a company that's looking to sponsor one student engineering team, in any high school or college event, which am I going to choose of the following?
- A group of high school students with little to no adult supervision, asking for $10,000
- A second group of high school students, with plenty of involved adults, asking for the same $10,000 or as much as I choose to give
- A group of college students, affiliated with a known organization and a known school, asking for whatever I choose to give?
I can tell you right now, it won't be the first one unless there's a really good reason not to fund the others. That's what you're going to look like to the companies. And especially if you have the attitude of "oh, it's only one sponsor, so it doesn't matter." Means you're going to have to fundraise awfully hard...
And if there is a tie between two of the first type of group, I'll take the one that has a history first. So the rookie will be left out in the cold.
Realistically, you want to keep your number if you can. And you want to get an adult or two. Especially, engineering types who know when to keep themselves out of a job the students are doing. See Dave's Kickoff comments from the last two years.
In short, my advice is, don't go the way I think you're looking to go, and keep what you can. Unless, of course, you hate yourself.
(Sorry, "if you hate yourself" is what my Intro to Solid Mechanics prof says if he's warning us against the hard way of doing something. It's rubbed off on me a bit...)