Pick a major that you think you'll enjoy. Don't pick one just to try and get a Type I scholarship. I received a Type II with Physics as my major (later changed to Aero Engineering, though). I don't know how it is at the school you're wanting to go to, but if a cadet at my school had any type of ROTC scholarship, even if it didn't cover full tuition, the school would pick up the rest of the tab.
BL: Pick a major you'll enjoy. If you pick something like EE, then end up hating it and wanting to change, you might not be able to without losing your scholarship.