Can you seek and adopt particular children?

Hello Glow, I have some questions about American adoption. Unfortunately google is being vague on some things or it tells me it varies by state, and specifically I'm a resident of Oklahoma if that's helpful to anyone.

My wife and I both have steady careers, I'm a traveling RT and she's ... well she does some type of graphic design stuff that seems completely random to me because I suck with computers, but anyway we're stable. We already have one biological son and I'm usually on contracts in different locations for 8+ weeks at a time and they both come with me. However, we do have a "home base" in Oklahoma via an inherited house/land we live on and my stationed hospital I work at between contracts.

We're playing with the idea of adoption, but we specifically have a desire to adopt a older child or teen and would love to find a transgender child. This came to mind after I had a trans teen patient who had a severe infection unfortunately, but she also had the most heart breaking story about being passed around in foster care and abused (and raped) because of her disposition. My wife is also transgender and has a eerily similar story. I had the pleasure of being the girls friend for a few weeks but she was transferred. That was all about year ago. I thought about her for a long time and have no idea where she is or if she's okay.

So my question is if you can specifically search for and select foster children/teens with a certain condition. Another is how does having a traveling career effect adoption? I know many traveling RNs and LPNs but none who have answers unfortunately. And really how does one even find a child that is compatible with your family? If these are rude questions by the way, apologies.

I really don't even know where to begin to look. So really any advice is interesting, thank you.