There's a lot of good stuff in the media browser, and you'll probably find it useful to jump straight to certain collections. However, if you drag the Media Browser tab to your shortcuts bar or Favorites tool, you'll only be bookmarking the Browser — it won't remember which collections you currently have selected.
However, you can use the History tool to get around this. Just choose the filters you want in the Media Browser (for example, Media Collection = "Logos Verse of the Day", Language = "English"). Now drag the History item to your Favorites tool, or to your shortcuts bar. Now you can quickly access that selection with just one click.
