Have you checked for a pit bull -centric mailing list or adoption place? Might be a good place to find someone who is interested in such a breed of dog, unless you prefer to find someone locally who you can visit often. Might also want to post in grocery stores, Wal-Mart, and in local neighborhood papers on the cheap-cheap.
Apollo is pretty cool. Why not find a small place with a fenced in yard that you can rent with a doggy deposit? Might also want to check into buying a home that can save you loot with tax deductible interest. First time homebuyers get great incentives and can sometimes get 105% loans. Check into two mortages, one at 80% and the other at 20-25% of the home's value. Your current management job and military experience will help you more than you may realize during the application process.
Me and my family have extensive experience in the real estate market. Can loan you a few starter books or help you if you'd like.