considering adoption and confused

[kitkatkc]

My husband and I have 3 children, and made the decision after our third child that I should not get pregnant again, as my pregnancies were increasingly difficult, and the babies were increasingly early, with our 3rd ending up in the NICU. I have had my tubed tied, as I couldn't risk our family or my health by getting pregnant again.
Since we got married, we have always wanted to have 4 children, and would really like to adopt, but I don't even know where to start.
We live in Kansas.
We would like to do a domestic adoption.
I have tried doing some searches for adoption agencies, but I don't really know how to start, or how to know if they are legit. We would really like to have our children close in age, our kids are 4, 2 and 1.
I know that Catholic Charities will not do adoptions with parents who can have children themselves, so I don't know how they would view my situation.
Does anyone have any recommendations for adoption resources in Kansas? We would be interested in a semi-open adoption. I was adopted, and I still struggle with not knowing my birth mom.
I'm sorry this is such a confusing post- I really don't know where to start. I know that we should start the process soon since it can take a while to get a placement.
Would having our own biological children be a deterrent? How about if we wanted to be able to exchange pictures and e-mails, but not have actual visits?