To open the dialog window of your media gallery and have it display only regularly-used files, you can click on the small black arrow to collapse the properties frame.

At present, there is no property or setting for having this collapsed by default and you would therefore have to manually request it each time you open it, however you can simulate that extra click by using the following javascript:

$j(document).ready(function () {
  $j('.DialogResizerArrowV').click();
});

To make it work in media galleries, please place it into the ~\CMSModules\MediaLibrary\Controls\MediaLibrary\MediaLibrary.ascx file.