So much depends on your wishes and the agency you pick!
As someone else stated, you are actually in the middle age range for adoptive parents.
It really comes down to what you are comfortable with and now long you are willing to wait.
After researching domestic adoption, and talking to dozens of agencies I decided that international was a MUCH better option for me. And at this point it's hard to imagine doing anything else.
If a private situation popped up domesticly I would consider it, but I would never pursue a domestic adoption of an infant/newborn at this point.
Personally, I find that International is much more stable and predictable then most domestic adoptions... if you have done your research! There is no such thing as a "sure" thing...but I think IA is MUCH closer to that then DA is. Again that's just my personal opinion
I'm sure there are a million people here that disagree with me
lol
If you aren't up to an Open adoption (F2F visits on regular basis, full disclosure of personal info) there are a good number of adoptions out there where Semi-open (letters & pictures sent directly or through 2nd party) is still an option..at least according to the emails I've received. But Closed adoptions are few and far between if that is what you really want.
Best of Luck