Welcome,
First, Army Legal Aid isn't going to be able to help you much. They're not set up to handle domestic parental placement adoptions. You're going to need an attorney with experience in this area.
The American Academy of Adoption Attorneys keeps it's member list online at
www.adoptionattorneys.com. Check the list for lawyers near you, call at least three and talk to them about their experience, services, rates, and your comfort level with them, etc.
You'll need to have a homestudy done, your attorney can help you arrange this or you can contact some local adoption agencies - again check their services, fees, and your comfort level with them, etc.
Depending on where you live, your total cost can run anywhere between $3 - $10K, possibly a little more. The military reimburses up to $2K in expenses post-placement, and there's also a federal tax credit up to $10K.
The good news is that you don't have to come up with a big lump sum - most will work with you. We did it when DH was E-6 AD/USN. We did save for a year before we started the process, ended up though that we didn't even touch the 'baby fund', just cash-flowed stuff.
HTH, best of luck, please feel free to ask questions. This board is a wealth of information!
Regina