Hi there. There are various of Message boards that you can use today, most of them fulfill your requests, so you don't need to worry. Setting that message board would include that you already have a place where you can host that script and domain for that host. Be sure to have that first.
PhpBB is a good choice, a well-established brand of forum script that has a large community of people ready to help you in the future, so we can choose that.
Anyway, feel free to hit me up so we can talk more about this. I am very responsive. All the best