The little guy in my avatar is my adopted son. Needless to say I've got some opinions on the subject

International Adoption: Most folks go that route in hopes of getting a younger child. We started the China process in 2006. At that point it was a 12 month wait. The wait is now 6 years plus. There have been a lot more rules and expectations put in place for international adoption. This is mainly to slow the abuse of the adoption process as there were lots of kids being 'trafficked", lots of false information and it had basically become a real money making racket at the expense of the kids and the folks trying to adopt. Yes the process on the US side is also a pain and pricey with all kinds of goofy forms to fill out. As you may note, Matthew, in my avatar is not Chinese. He's from Liberia. I've told the story too many times, but the process fighting to get all the ducks lined up for him took almost two and a half years after we'd gotten him into the country. The system is very rigid and doing anything that doesn't fall into the right place in the line, can really throw the system off.
Domestic Adoption: Lots of folks willing to help you with that too, for a price. When the China adoption stuff kept extending out, we looked into domestic adoption. Costs are roughly the same. The process was a bit faster. We wanted as young a child as we could get. We worked with a crew that helped expectant moms who were giving up their babies, choose a family for their baby. Interestingly enough we got picked before we'd even finished all the paperwork. We'd been open to a child of any race and were picked by a young black woman. This happened during the time my wife was in Liberia volunteering as a nurse. She 'found' Matthew abandoned at the same time this birth mom picked us. Again, money was spent, and in the end she chose to keep her baby. We at that point would not have been allowed to adopt that child as Matthew was being adopted. Couldn't do 2 at once according to the rules.
Adopting an older child: I'd suggest strongly that your wife does some research on 'reactive attachment" issues with older adopted kids. I've worked with 'troubled teens' most of my adult life. Many of them were from failed adoptions and reactive attachment was always one of the biggest issues. Sadly, the damage done to some of these kids in those early years before they are adopted by a family can be really hard to deal with. Those first 4-5 years can make all the difference for a kid growing up. And you can be the best adoptive parent in the world, and you still might not be able to get past it. Because of this, my wife and I wanted as young as we could get. Matthew was 4 days old when my wife 'found" him and was completely in her care at 10 days. We joke that he suffers from 'active attachment' as we were able to bond with him right away.
Bottom line is do the research. Understand it's going to cost you money wise more then you'd probably think. And keep in mind that all the other stuff that goes with adoption is out there in the future. That includes health, and mental health stuff you may not have any history on. In our case Matthew had a bi-lateral cleft lip and palate that was the obvious reason he was abandoned. But it turned out he also is profoundly deaf and because of a cleft larynx, still gets his food through a G-tube in his stomach.
Trust me I'm not saying don't do it. Matthew is my child as much as our bio kids, and I feel absolutely blessed to have him as my son. I really don't even like saying he's adopted, although because we're white parents of a black child, it's fairly obvious

I wish you all the best in making it happen however you choose to do it.