One of my favorite approaches is to create dynamic classes for the body element.

So: 

    <?php
      $app    = JFactory::getApplication();
      $menu   = $app->getMenu();
      $active = $menu->getActive();
      $class  = $active->alias . " pageid-" . $active->id;
    ?>
    <body class="<?php echo $class; ?>">

Some examples of what the above code will produce is:

Home page:


    <body class="home pageid-13">

About us page:

    <body class="about-us pageid-15">


Now you can create custom specific styles per page, using the above classes.