I'm new to this - please forgive my ignorance

Hague Convention Countries usually have additional requirements for those adopting internationally from their country. Each Hague country's requirements are different, you will need to look at the countries you are interested in to see what their requirements are. I have heard of families adopting internationally while living abroad, but I do believe that it is more difficult. Most likely you will have to find out what your country of citizenship's requirements are for international adoption and also follow those requirements. Depending on the country you adopt from and your country's requirements will depend on what kind of passport your child will have. I'm adopting from Bulgaria, my child will become a US citizen when she passes through customs based on the type of visa she will come home with.