Very misleading,
1 Passport is not an issue, I have UK passport, all they want is that you have a passport that will allow unlimited exit and entry to US.
2 US Citizen only required for government and security sensitive jobs. Pilot jobs not an issue.
3 Suggest a green card or sponsered by an employer. Sponsership has become very difficult due to plenty of available manpower in the US.
A lot depends on what it is you want to do and for how long, I initially had a student visa which allowed INS authorised employment as long as I remained in study. (I did my Aviation Science Degree and took 8 years to do it, lots of flying!.) I ended up getting married to a US citizen and got a green card so now its a no brainer.