From what I have heard through those I have talked to, and my experience in the process so far, the best thing you can do is go find your local officer recruiter, and start pounding through the grunt work. Getting transcripts, getting letters of rec, filling out the paper work, drafting a motivational statement and taking the ASTB. It all takes time. In the interum, you can ask all the questions you can think of, do the serious career thinking, and talk to anyone and everyone you know who was in the military. The only expense to you is the transcripts.
As to your chances, "The needs of the Navy," dominate if / when you get in. Going one on one with your recruiter, spelling out your goals, and simply doing it is the only way to get it done. You have questions he has answers.
Do some searches on the forum for ASTB gouge, stats on acceptance and rejection, as well as stories of life as a NA/NFO, military life, and your future in general. Go into the process confident, informed (as much as can be expected) and ready to do what it takes to make your goal (if its to be a Naval Aviator) come to reality.
P.S.
www.navy.com or
http://www.cnrc.navy.mil/ should be able to put you in contact with the closest officer programs recruiter.