I have setup Fireboard so that only registered users can write posts and public users can only read, which works great. But, what I want to do is create a public write forum where anyone can write posts. This allows the public to interact with my registered members, but the registered members have the benefit of member forums, which are clean from spam/garbage.

How do I setup Fireboard to do this?

I want the public/members to be able to read everything, but only allow the public to write to one forum!

Interesting. I haven't done this myself. Have you tried creating a new category, adding a forum to it, and then adjusting the Access Levels so that anyone can write.