How can I show selected items without exposed filters?
Alternatively can you use "Promoted to front page" under "Publishing options" while adding content. This content will be the contents you need as important and will be visible to users.

Below that your view with exposed filter will be shown.
In View "Filter criteria" you can ADD "Content: Promoted to front page" option to show the non promoted contents, and also exposed filters. 

You can apply this logic in your content type also, if you need specific fields such as "Mark as Important", give it some Boolean value and select it in filter criteria as mentioned above. If not can be added from "Contextual filters".