Sounds like you have it together on getting support & custody. That's good to do it thru the coursthouse. I did. I have sole custody and guardianship. I don't know what it's called where you are, but sole guardianship is very important if you don't want to have to trck him down to sign for stuff.
Right now, my ex has reasonable access. It works for us, and so far no need for the courts to define it. He hasn't asked to see her alone, visiting with me there seems to work well for both of us.
I"m sorry you're going thru this. I think you are oding the right thing going thru the legal system rather than just trying to track him down though. If he is really ging to be involved in his child's life, that has to come form him. I personally wouldn't oush on that either.