Read up on HTML forms. You aren't sending any values from the form into the URL. Each <option> tag needs to have a "value=''" parameter....
Plus, why not just use hidden fields:
<?php ?>
<form name='form1' method='get' action='results.php'>
<input type='hidden' name='filter' value='<?php echo $filter_recordset1; ?>'>
<input type='hidden' name='search' value='<?php echo $search_recordset1; ?>'>
<select name='select' onChange='this.form.submit();'>
<option value='name'>Name</option>
<option value='family'>Family</option>
<option value='level'>Level</option>
</select>
<input type='submit' value='Sort' name='submit'>
</form>
~Brett