Please do look at joining the military as an enlisted member, since you don't yet have your citizenship. Like has been stated in this thread, it will help you achieve citizenship faster.
If you'd prefer the longer route of getting your citizenship first, you run into the risk of being too old for pilot training. I think the cutoff for off the street applicants (which is what you would be) is 25, but I'm not certain. If you're already in the military as an enlisted member, the age limit is increased.
Your background can bring a lot to the table as a service member. I served with lots of members who were immigrants and they brought perspective, language and cultural skills that none of the rest of us had. Several times when we rolled into various foreign places, it was our immigrant service members who provided the most effective ice breakers when interacting with our hosts.
Start talking to a recruiter.
As for which service produces the best pilots? Well, I've met great Air Force pilots and crappy ones, same for the Navy and Marines (I was Navy). I happen to like how the Navy does training better, but that's just me and how I learn - Navy training us MUCH less structured. Overall, all the services produce excellent pilots and all have their pros and cons. If you want the snazziest uniforms though, go Marines or Navy
