I wouldn't discount your social system and local church-based agencie. Lutheran Services, Catholic Services, and your county services may be good places to start. That said, that's where we started and in the end, we adopted our middle child (son) from South Korea. Lots of domestic charitable agencies weren't interested in us - because I was too old, too fertile, had a bio child all ready...
BUT the main reason we went w/ S. Korea was because my husband was adopted and S. Korea's practices matched up with how my husband thought adoption should be handled. Who would I be to argue with my adoptee spouse about that!?
It took about 6 months to referral, then 6 months more to bring him home to us. The referral wait would be longer for a girl, because most adoptive parents ask for girls, if they have a choice. And the process is taking a bit longer now for other reasons. But after referral, wait times are fairly predictable.
Children in S. Korea are in foster homes (as are SOME children in China), and are VERY well cared for. Our son was 11 months old when he came home and had a very diificult transition - from his point of view, it was as if we'd stolen him, and he acted accordingly. He put up a FIGHT- biting, kicking, hitting, puking on, well, ME mostly - & he wouldn't let his Daddy put him down for weeks.
He's well bonded now, a little over a year later, and is a lovely child, but is temperamental and has several tantrums/day. It's getting better, and he's only 2, so we're in tantrum territory as it is. This is a child who was in an orphanage for, at most, 3 days and who was deeply loved in his foster home. But a lot of it is his temperament.
Like with bio kids, you get who you get and temperament can really affect adjustment, regardless of where the child spends her first months. Fortunately for us, his big brother has a similar temperament or we would have been completely at sea. So - it's been harder than I could have imagined. But I can't imagine NOT having him in our family either!
Still, after all I know now, if I were to adopt again, I'd look harder at the US - if only because the child wouldn't have to deal with the stress of EVERYTHING being different (how people look, smell*, speak [*because the food is different]). Not all children in foster care are at risk adoptions and not all were abused.
But you have to do what's right for YOU. Honestly, you may just "know" -deep in your heart - when you find the right way to go.
Whatever you decide to do, don't rely on your agency for all of your information. Join a yahoo group (or something) of parents who have adopted in the way you decide is right for YOU so you can get a good idea of how to prepare yourself and your sons, as well as what to expect with your daughter.
Best of luck to you!
This is the agency we went through:
http://www.aacadoption.com/