My boys are a mix of bio and adopted - our almost-4-year-old came home from Korea 3 years ago.

We used Holt International as they are one of the largest agencies in Korea and we have a family friend who brought her two children home from Korea through Holt over 30 years ago.
We chose international adoption over domestic for a lot of reasons and after lots of research. The primary reason we chose Korea is that my DH is half Korean so we have a cultural link to that country.
While it is expensive, the cost is spread out over a little bit of time and you have a pretty good idea when you start the process of how much you'll need to pay and when. To keep it relative, it's not much more expensive than having a biological child via c-section with no insurance. Plus, there are tax incentives (the adoption tax credit (refund?) is over $10k) and grants if you qualify.
I think the most important thing to do first is decide if you want to adopt domestically or internationally.
We went through Holt's Waiting Child process and our lttle man came to us with a heart condition which has since been resolved into a medical non-issue. It's a humbling experience but something you need to do is take a good, hard look at what you believe you are willing to handle from a "special needs" perspective. We thought long and hard about what our limits were and what kinds of issues we could handle while still growing OUR ideal family.
We took "Parents in Process" classes through Holt (they're mandatory) and they were very helpful in giving us a lot of insight into things we may never have thought about.
There are so many facets to adoption and it can be overwhelming! Trust me, I know!

Take your time, keep gathering info, and eventually one path will feel right.
ETA - Keep in mind that most agencies will discourage you from adopting out of birth order and very few will even consider letting you displace your oldest child so you'll most likely be looking to adopt an infant. This might make domestic adoption harder as most infants are placed into families chosen by the birth mother and they "usually" want to put their child with a young, childless couple. There are exceptions to every case but this is the general rule.
ETA (again!) - Come browse the Holt adoption forums - they're open to potential adopters, those in process and those who have already brought their children home. Doesn't matter which agency you ultimately select. Tons of great info with a large crowd of helpful folks:
http://www.holtinternational.org/forums/ (I'm GloriaNJ over there - spend most of my time in the post-adoption forum)