Looking for Advice

Hope I'm in the right area! My boyfriend and I are only legal domestic partners in MI, because of this we realize that we can probably only adopt as a single person and then later on the other can adopt the child too. We are just starting to gather information for adoption and are a bit lost as to what to do/where to go. We are interested in adopting a newborn/baby privately without an agency, as we've learned from friends who have adopted this can be a more cost effective method and we already have a 4 1/2 year old and feel that getting an older child would not be good for him. Are we right in thinking that a private adoption is more cost effective or should we find an agency? What is the best way to start the process or begin looking for birthmothers? Is there a particular place we should be going or should we contact an adoption attorney? Any advice would be greatly appreciated!