How to create pages that contain selected posts in a custom order.

Hello

I’m creating a sort of “architectural article library”.
I want to be able to create a page that it will be a proposed “reading list”, or a collection of post if you like. From the admin UI, be able to add the post that it should contain and arrange them manualy, like for example how “Post Types Order” plugin does it.
One important thing is that every post can be part of many reading lists.

Any ideas how I should do it? Is there already a plugin or something that does it?

Thanks