Just use the Views module to create a block display. And within the block settings specify that you only want to show it on the "front page". The fields to be shown are probably only the title of the nodes you want to see included in that block. with that you've reduced your question (challenge) to selecting the appropriate Views "filter" and "sorting".
To filter your nodes, you could add an extra field to the content types (like your "News"?) you want to see included, whereas that field is just a boolean to yes/no indicate if it should be shown in that block.
If you'd want to make it a little more flexible (dynamic), you could also use the Flag module, and allow authorized users (with appropriate roles to set such flags) to flag whatever should be included in that block. Your view would then become a similar list of nodes that were "flagged".
Enough options to pick from?
PS 1: I'm assuming this question is about Drupal 7 ...
PS 2: for D8, Views is in core ... and for Flag there is a 8.x-4.x-dev release, for which the current status is "Under active development, but not yet ready for production."