No scale on your major. You can basically major in anything you want.
Basically, your class rank is comprised of your grades in your classes, your military grade and physical grade.
Branching is carried out according to the "needs of the Army". Right now the Army wants their officers to be happy - so they have added incentives. One incentive is to extend your ADSO in favor of the branch you want. Aviation already adds extra time on to your ADSO so you could be obligated for many years.
In branching, West Point is bound by law commission 80% of their graduates to Combat Arms branches. Aviation is a combat arms branch. It is one of the top 3 branches in popularity.
If all you want to do in the Army is fly choppers then go get your college degree and sign up as a Warrant Officer. You will then fly your whole career.