Which does she like? Can the school give her the opportunity to try them? Does the school band have a place for these instruments in it? Maybe only flute is on offer. If you give her private lessons and she progresses well, the school might include her in concerts as a featured instrumentalist at a later date. With these wind instruments, presumably what you learn on one can be transferred (at least in part) to another. Certainly, learning musical notation and reading music will be transferable. Does she have good breathing? These instruments will all require a good deal of breath control.
No matter which instrument you choose, it will take a GREAT DEAL of practice to achieve a scholarship.