Our son is adopted (we used Adoption Works in the Dallas, it was formerly called Christian Services of the Southwest) and we will likely adopt again in the future. There are tons of agencies out there, so I would just start searching online for info. Each agency has it's own parameters... most will not "put you low on the list" because you already have kids. For lots of agencies, they simply provide the prospective adoptive parent information (in the form of a scrapbook or paperwork that you have filled out - not your personal info, last name, address, etc. but what you do, what your family is like, why you want to adopt, if you have kids, etc.) to the birthparents and they choose the couples they would like to consider. That is the way our agency worked - there was no "waiting" list - if you got your paperwork in and a birthmother picked you the next day, that was that. For those agencies, it's just about which couples the birthparents are drawn to and what kind of family they want to place the child in. Like I said, do some research and find out the kinds of things appeal to you in an agency. The initial paperwork will take at least a month or two to get together (references, background checks, etc.) and after that the timeline depends on the agency and how they do things.
Our adoption went beautifully... there were ups and downs, just like there is with pregnancy, but we have loved the outcome. We have a very open relationship with our son's birthmother and her family and it works really well for us. It's different for everyone, though, and each agency will likely specialize in either open or closed adoption, so that will be part of what you base your agency decision on. Once a baby is placed with you, there will be a 6 month period until the adoption is finalized in court (this is how it works in the state of Texas). The $10,000 tax credit has some eligibility requirements, but you can google all the info on that - just look for Adoption Tax Credit. We got part of our credit this year and it is GREAT!
Also, in response to another post regarding money... I would be hesitant to go with an agency that requires all the money up front. Our experience was different - there were fees assosciated with the application, but we did not pay the rest until our adoption was finished.
Good luck! It's an awesome experience!