Your best bet is the Army due to pure numbers. The Army has a lot more helicopters than any branch. It's also the only branch that you can apply to fly as a Warrant Officer without a college degree.
The program is very competitive, if you have decent grades and some college your chances are a bit better but plenty of applicants do have degrees already.
You can apply to the Army's Warrant Officer Flight Training right now. It is highly competitive and is a rather lengthy process to endure. But if you are willing, and can find a Recruiter who will process your paperwork, it's a great way to go.
You will have to take the ASVAB as well as the AFAST (Flight Aptitude Test). If you pass those, you will need to take the standard physical at MEPS, and then a follow up Class A flight physical. Then you must prepare a packet for the selection board.
You must appear before the board and then they will determine if you meet the criteria to attend WOFT. But from the time you apply to the time you ship can take upwards of 12 months, so be prepared for it to last a while.
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