My advice is to check out the county before you do anything else. I don't know where you live but if you are in the U.S. there are some awesome benefits for adopting through the county.
DH and I had no clue about the fact that it was not only FREE but that the government will continue to help support your child until they are 18. The AAP (Adoption Assistance Program) was put into effect a few years ago where the President signed a bill making it so that the government will reimburse YOU the costs of raising the kids. (It's a set monthly reimbursement of approximately $500). This program was put into place as an incentive to encourage people to adopt. This benefit does not apply to those who adopt throuigb private agencies.
Dh and I had no clue about any of this, of course, and we found out by accident. Long story short, we were adopting our dd before she was born privately. The adoption went bad after the baby was born when the mom changed her mind after seeing her. After we were out of the picture, CPS stepped in and deemed birthmom unfit and took the baby. DH and I ended up with her after all (It wasn't easy) and we have been fostering her as we are in the process of adopting her. We've had her 8 months now. We learned about all this through our own experiences.
Going through a private agency you can expect to pay upwards of $25,000 for a domestic adoption and upwards of $30,000 for a foreign adoption.
Through the county you will get a baby and not have to pay a cent. AND you will be reimbursed approximately $100,000+ while your baby grows up. (Dh and I are starting our dd a trust fund and feeding it for her future with these funds).
It is true that the county does deal with alot of special needs children but understand that these kids are normal 99% of the time. Our dd fell under the category of special needs because her mother , come to find out. Keep in mind that the women that give their babies up through agensies often do questionable things during their pregnancy, (ours did), not just the ones from the county.
Knowing what I know now, I would never consider adopting through a private agency because of cost alone. The reimbursement money through the AAP is a plus, but we would adopt through the county anyway. Their babies are just as precious and the wait is the same. Good luck! Any questions, my email is
CelinaEve@aol.com
Feeling totaly overwhelmed 
