I am current military.
The first thing i would do is obtain your private license from a small FBO near wherever it is you live. This will allow you to get in the air and see if you truly love flying and would like to make a career of it (i am not doubting you will love it) It will also allow you to shop around and find the best rate and the best instructor to get this accomplished. The VA will not pay for any part of this rating at all, so get it where you want to get it.
As for RAA, I have not been there but here is what I can tell you. By attending RAA it will cost you more in the long run and not put you any further ahead then the others you are competing against. What it all comes down to are ratings are ratings and hours are hours, just because an RAA grad payed 80k for his ratings and hours does not make him a more competent qualified candidate then someone who payed 20k for his ratings and hours.
Use your VA benefits! They are not as limited as you might think. Attend a school that is VA approved after your private and they will pay right around 50 percent of the cost. They say 60, but the school you train at will give you more than the minimum the FAA requires for the rating, and the VA pays 60 percent of the minimum, so the extra hours are on you. But overall 50 percent is not bad at all, especially when we are talking tens of thousands of dollars.
You do not want to start your career where your first job will pay somewhere in the 20k range per year and at the same time have a $600 dollars per month loan payment for the next 20 years. Plan on paying roughly $100 dollars per month for every 10k borrowed. Seeing how you are recently seperated from the Army you should have a little cash saved up, use that for your training.
Schools that i would reccomend that will not take all of your money.
ATP- I believe cost around 44k and will give you all of your ratings, you can instruct for them for approximately a year after your last rating and end up with around 1000 or so TT and 600 or so ME. They do not accept VA benefits though so i would shy away for just that reason alone. They are a great school though
Ari-Ben- Probably my first choice. The school charges around 31k for the same exact ratings as the others and you can still instruct after your last rating for a year and end up at the 1000 and 600 mark. They are VA approved and will walk you through the out of pocket cost. The difference between them and ATP is that Ari is not a chain as ATP has locations all over the country. Also ATP has alot more money so their equipment is better maintained and newer and their facilities are nicer. With that being said Ari has nice planes and a nice location and their equipment is more than safe and airworthy, well worth the 14k savings.
Local VA approved FBO- You might have one at your home airport where you get your private. You can get a great deal with them sometimes with block time and just stick with the small environment and the one on one attention.
RAA and others promise job placement etc. however that means nothing and i wouldnt even care about that promise. Pilots get hired all the time from all over due to their experience and the overall way they present themselves through the entire interview process. ATP has graduates hired into the regionals and others every month. Just last month i believe that Ari had i think 6 instructors hired by Xjet and i think some others at Colgan.
Just my two cents on the issue, do not get caught up with the glamor and what the recruiter tells you on the phone or how nice their website is. What i looked at for my ratings was...Are they VA approved? If the government is offering it, i am taking it. Are they the cheapest? A rating is a rating is a rating. I can fly the worlds most beat up cessna 120 taildragger at a rundown FBO just as well as someone at a large academy who is flying a 2006 172 skyhawk SP with Garmin G1000, and the regionals and others....they will not care what you flew. Since they do not care where you flew, what you flew, or anything else of the like why not save all the money you can. Your Commercial Multi engine rating will not say where you got it or how much you paid. Let your skill show for itself, that is what will pay off at the interviews.