form + output on same page + form remember last values

Hi ! I want to make somethin like this

At first i have a menu hook so i have a path like http://host/mymodule/listsomething . At this page i have form for making filter settings and below of this a result table with the result of this filter. Something like a checkbox "voted good by others but not me" and so on and so on. If i now set the filters and press the go button on this form the page regenerates and the listing should show the filtered result.

At the moment i have a solution with using $_GET variables. The submit function reads the form_state values and generates the Get parameter string to add it then to a url.
Via drupal_goto i go to this url and everything is fine. But i read about the form api and that this is maybe not the right and perfekt way. So i tried working with the form_state variable on the form itself by making something like

$form['title_filter'] = array(
	  '#type' => 'textfield',
	  '#title' => t('filter by title'),
	  '#default_value' => $_POST['title_filter'],
	  '#value' => $_POST['title_filter'],
	  '#size' => 20,
	  '#maxlength' => 30,
	);

or

$form['title_filter'] = array(
	  '#type' => 'textfield',
	  '#title' => t('filter by title'),
	  '#default_value' => $form_state['post']['title_filter'],
	  '#value' => $form_state['post']['title_filter'],
	  '#size' => 20,
	  '#maxlength' => 30,
	);

But no success with this ! ;(

Any help and hints are Welcome !