Bless you. What a wonderful choice to make! Don't feel guilty for having specific criteria you want to match in your search for a child. It's better to be picky and adopt than not to adopt at all! Try to be open-minded, though, as you do your research; what you learn may cause you to change your mind about some of your criteria.
To answer some of your questions...
It would be pretty tough to adopt a caucasian girl under 2 from the U.S. We found that domestic adoptions are very competitve (you have to advertise yourselves as prospective parents), and the wait is indefinite. However, if you are open to a non-caucasian child, you would definitely be able to adopt a girl under 2 with minimal or no health problems from another country. China, of course, has plenty of girls available for adoption, though the wait has become quite lengthy. It's worth the wait, though! (Our four year old daughter is from China).
You didn't explain why cacausian is important, but don't forget, it seems like everyone is adopting internationally these days (even the movie stars are doing it). If you had a child who didn't look like you, it's not like it was years ago. People are accustomed to it now (with a few exceptions) and for the most part are very accepting of it. Between just our friends and neighbors, there are a total of 12 non-caucasian adopted children, and these are NOT people we know because of adoption (obviously we know many more families through adoption circles).
In my experience through my research and with my friends who have adopted, international adoption is NOT more expensive than domestic. There are definitely countries that cost more than others (for example Korea is more than China), but I read that domestic is just as expensive. As far as cost goes, we found that the money was always there each time we needed to pay a fee or pay for travel. It wasn't as bad as we thought it would be (I really think God provided what we needed).
Because you want a healthy child who is caucasian, I feel I should mention if you choose the international route that many European children who have been placed for adoption suffer from fetal-alcohol syndrome and other drug-related problems. I'm not being prejudiced, it's just a fact. Although, our neighbors' daughter is from Russia (she's 4 now) and she is perfectly healthy. But, they are having problems with the baby boy they adopted later.
If you contact an adoption agency, they will be happy to send you literature. And of course, you can always look online. A lot of agencies have really good orientation classes as well. For international adoptions, I highly recommend Holt International http://www.holtinternational.org/ They do not have any offices in Texas, but you can work with a local cooperating agency that works with Holt.
Whatever you do, make sure you use a reputable agency. Don't try to find loopholes or shortcuts. All kinds of bad things can happen if you try to "cheat the system" (as did with two different families I know). Based on the experiences of multiple friends, I also recommend using an agency as opposed to a lawyer.
Good luck. Pray about it too! If you have any other questions, please free to send me a personal message. It's a wonderful thing. I have one adopted child and one biological child and I'm so glad I was blessed with experiencing both.
If you want some inspiration, motivation, etc. check out one of the millions of blogs online. Just type in adoption blog and you'll find great reading and photos from families who have done it or are in the process.
~A.