Another recommendation for Jennifer Fairfax. I have heard her present at adoption workshops and have met several of her clients, all extremely happy with the service she provided.
There is a DMV area non-profit called Families for Private Adoption (FPA) which provides education and support to those pursuing domestic independent adoption. FPA surveyed its new parents in 2012 to get answers to the time and cost questions. The median answer for cost was in the range $20 to $25K, and the median answer for time was 12 months. (By definition for many it will cost more and take longer, and there is no guaranty of success). The survey write up is under the FAQ tab on ffpa.org.
Depending on your income level, there is the Adoption Tax Credit which offsets the costs of adopting, and is designed to encourage adoption.