Sharon, I don't know about the specific postings you're talking about, but I will warn you that there are a LOT of scams out there. I would recommend an agency-assisted private adoption. In that situation, any potential birthmom is referred to the agency you're working with and they do the sticky job of confirming pregnancy and assessing bmom's preparedness for placement. Then, if all is well, you proceed with an attorney-facilitated adoption.
I see you're in NH. I know of an agency in NY that does this type of placement, but I don't know if they work with people in NH. If not, they can probably refer you to an agency that could help you. The agency is Adoption STAR:
www.adoptionstar.com.
Hope that helps!