> click a button (filtering for, say, vertical or programming
  > language) and get transported to a repository that has a baseline
  > level of merit (say, at least three stars).

Below is a search for repos with at least three stars sorted by date updated. You can filter by language by clicking a language listed on the left side of the page.

https://github.com/search?q=stars%3A%3E2&s=updated