Hi ! I am going to adopt a pet from the animal shelter soon. I believe I would like a dog 
That is very nice, a shelter is a good place and there are actually rescue groups that you can call like the Humane Society.
Yes, I have found some rescue groups locally, however, they charge a very hefty rehoming fee.  
Well there are other animal rescue groups too, they all are mostly run by volunteers, but they are trained to handle medical problems and such.
After Katrina, Pitbulls and Parolees ( a local tv show) offered services to Katrina victims who had to leave their pets behind. 
There is one called Best Friends Animal Society, it was originally a church but it became a charity in 2003, that might be another option as well.