If you want to create a meeting type for a specific group of people, that will now show up on your Public Meetings Page then, naturally, you would want to make it private. This can be easily achieved either while creating or while editing a meeting type.
In the "Info" section of your Meeting Type, at the very bottom, there will be a toggle button for your Meeting Visibility. When it's green (toggled to the right), the meeting is public, When it's gray (toggled to the left), the meeting will be private and accessible by link only.