1) First, add a new article field named, let's say, edpick. Make it a checkbox. Uncheck the options for making it user submittable/editable since you want only editors to be able to choose these.
2) For articles you want to make editor's picks, edit them to check the box.
3) Create the new page at Admin -> Themes -> Custom Pages. In the content we'll use a toplist. Go to Admin -> Themes -> Toplist Generator. For the filtering condition, type
edpick = 'edpick'
. In the box for display content, let's use <p><a href="{TRACKLINKURL}">{LINKTITLE}</a></a> - {LINKDESCRIPTION}</p>
. If you want something more fancy you can use the regular article bit by typing [INERTFILE=linkbit]