At the moment for our state Taiwan is the fastest program but unfortunately also quite expensive as the in-country fees are pretty high and in US dollars.
The least expensive is Thailand as there are no local fees in Thailand, you only have to pay your state assessment fees here in Australia. Plus the travel costs in 4 years or so when you travel to pick up your child.
Other countries are a much longer wait that Thailand or Taiwan. Some states are involved in a special needs trial with China which I understand is the fastest of all, and apparently the children have very minor needs, not the major ones you read about Americans adopting. But only a limited number of states are involved so it wasn't an option for us.