What is the best way to collect and report statistics from within views 3's exposed filter?
You can use GA Push module:


  GA Push offers an API to enqueue informations that are sent GA
  servers, and three submodules to track browser events (using jQuery),
  form validation errors and log exceptions.


Instead of saving the data in your custom table you can just send it to Google Analytics.

Collect your data in your PHP code and send it like this:

      $push = array(
        'eventCategory' =&gt; $category,
        'eventAction'   =&gt; $action.
        'eventLabel'    =&gt; $label,
        'eventValue'    =&gt; $value,
      );
      ga_push_add_event($push);


You may hook on the form submit instead of adding PHP code to the view.