I usually use both options in the navigation bar... (I realize this is not exactly what you're asking.)
So
Forums default page
Forums
New posts
When entering the forums section, this will be the default page users will be taken to. They will be able to access the alternative page via sub-navigation options.
So, as the default, pick whatever you prefer and then add options to your navbar. I generally use Forums as the home page with a couple of widgets in the sidebar and the navbar changes..
No, I'm talking about using New Posts as the default forums page. In this scenario, when someone visits your website the home page is new (unread) posts, not all. And when you click the logo, same. Nothing to do with nav bar.
Yes I understood what you were asking and I don't think you can change that the way you want to. If it's a non-logged in visitor or member, "new" posts are all posts. If it's a logged in member, "new" posts are those the member hasn't read yet. That's by design.
When I set it to Forums I see all posts because they use the nav to get there and I altered it already like you said. The problem is with New Posts as homepage they use the web address to get there. So trying to find a way w/o altering the actual site URL.