We've adopted twice from China and I've been following IA since 1995. I would recommend a couple of things. First, order the Report on Intercountry Adoption from ICC at http://www.iccadopt.org/
It costs about $30, but will be well worth it, as it details program and agency requirements quite well.
Pick up a few issues of Adoptive Families or Adoption Today to get a feel for IA issues and programs.
Find a local "support group" for IA families. Most have events that are open to people who are just in the decision phase. My local group just hosted its annual Adoption Fair, with a bunch of agency reps, adoption attorneys, social workers, etc. It's a good way to get a lot of info quickly. We also do an annual panel discussion with families who have adopted from various countries recently discussing their experiences.
Costs vary considerably. We spent about $15K for each of our adoptions. To do it again today would be a bit more expensive as the homestudy requirements have gotten more burdensome. A lot depends on the travel. Many countries require two trips, which jacks up the cost. Some Eastern European countries run around $30K or more for agency adoptions. Haiti, I believe, is one of the least expensive countries, with costs running around $12K. Most South American countries are on the expensive end. Middle Eastern countries tend not to allow international adoption at all.
While the cost is intimidating, you can do it if you put your mind to it. We managed to save the money for both our adoptions and we don't have big salaries. Other people refinance homes, take loans, borrow from relatives, sell assets, etc. There is also a 10K adoption tax credit, which helps, but you have to put the money out first.
As for picking a country, that's a very personal thing. You will need to feel an affinity for your child's heritage because it will be important to incorporate that heritage into your family. That may narrow it down a bit. Some people feel very strongly that they want a child that looks like them, so often that dictates the country. Countries all have unique requirements for adoptive families, like religion, length of marriage, income, prior marriages, other children, weight, etc., which may mean you aren't eligible for some programs. The children available for adoption tend to vary with the program. For example, if you want a very young healthy infant, there are very few countries where that is possible. Some countries allow you to select gender but others do not. Some countries require that the child have medical issues in order to be free for adoption. Certain medical issues, like FAE/FAS or Hep B exposure are more likely in some countries than others.
We picked China because we didn't care what the child looked like and we feel an affinity for the country. We have a fairly high population of Chinese people in our area and knew we could incorporate the culture into our families easier than other cultures. We wanted a healthy child, but weren't fixated on getting a young infant. We preferred to adopt girls, and that's easier in China. We also liked the system, which is free of corruption, and is a civil procedure rather than a judicial.
Good luck and feel free to ask anything.