BuddyPress.org

The login stuff should be easy, just modify this plugin to go to activity instead of profile: https://buddypress.org/community/groups/bp-redirect-to-profile/

I think there’s a similar plugin for redirecting after log out. Although, I think the default log out action is to send you to the home page.

To get the landing page as the home page, you can either modify the index.php in your theme to be what you want. Or you can make a page template and set that as the home page in your WP settings or…I think there’s other ways, but that should work.