Best way for including javascript/jQuery OnLoad in EVERY page on my site
Please read Managing JavaScript in Drupal, specifically the section on Behaviors. You'll need to do something like this:

(function ($) {

  Drupal.behaviors.exampleModule = {
    attach: function(context, settings) {
      var bgs=["bg1.jpg", "bg2.jpg"];
      var bgr=Math.floor(bgs.length * Math.random());
      $.backstretch(bgs[bgr], { speed: 1000 });
    }
  };

})(jQuery);