sorting results with sub categories

I have a category table and I have subcategories that are defined by parent_id which links to the main category id which is stored in cat_id

table category

cat_id PK int
parent_id int
category char

I want to add something to only show pets in cat X and in sub X

<?php
include 'config.php';
$domain = "http://www.rksdesignstudios.com/clients/critterclassifieds/pets.php";
?>


<p>
<form action="<?php echo $_SERVER['SCRIPT_NAME']; ?>" method="post" name="action">
<label><b>Sort by:</b></label>

      <select name="sort">
        <option value="name">Name</option>
        <option value="date">Date</option>
        <option value="id">ID</option>
        <option value="owner">Owner</option>
        <option value="category">Category</option>
    </select>
then
    <select name="ascdesc">
        <option value="DESC">Descending</option>
        <option value="ASC">Ascending</option>
    </select>
and show
    <select name="max_results">
        <option value="5">5</option>
        <option value="10" selected="selected">10</option>
        <option value="20">20</option>
        <option value="50">50</option>
    </select>
    <input name="action" type="hidden" value="go">
    <input name="submit" type="submit" style="float:right;" value="Submit!">
</form>

<br />
<label for="pages"><b>Page:</b></label>
</p>

<?php

if(!isset($_GET['page']))
{
      $page = 1;
}
else
{
      $page = $_GET['page'];
}


$max_results = 10;

$from = (($page * $max_results) - $max_results);

$total_results = mysql_result(mysql_query("SELECT COUNT(*) as Num FROM pet"),0);

if ($total_pages%$perpage)
{
        // has remainder so add one page
            $total_pages++;
}
$total_pages = intval($total_results / $max_results);

if ($total_pages%$perpage)
{
        // has remainder so add one page
            $total_pages++;
}
if($page > 1)
{
    $prev = ($page - 1);
    echo "<a href=\"$domain?page=$prev\">&laquo; Previous</a> ";
}

for($i = 1; $i <= $total_pages; $i++)
{
    if(($page) == $i)
      {
        echo "$i ";
        }else{
            echo "<a href=\"$domain?page=$i\">$i</a> ";
    }
}

if($page < $total_pages)
{
    $next = ($page + 1);
    echo "<a href=\"$domain?page=$next\">Next &raquo;</a>";
}

// alternating row colors
$color1 = "#f8f8f8";
$color2 = "#cccccc";
$row_count = 0;

if (isset($_POST['action']))
{
      echo "<h1>SORTING ENABLED</h1>";
    $sort = $_POST['sort'];
    $ascdesc = $_POST['ascdesc'];
    $max_results = $_POST['max_results'];
    $category = $_POST['category'];

$sql = "SELECT p.*, c.category FROM pet p, categories c WHERE p.category = c.category ORDER BY p." . $sort . " $ascdesc LIMIT $from, $max_results";

echo "<h2>" . $sql . "</h2>";
   $result = mysql_query($sql);
}
else
{
$sql = "SELECT p.*, c.category FROM pet p, categories c WHERE p.category = c.category ORDER BY p.id DESC LIMIT $from, $max_results";
$result = mysql_query($sql) or die("Bad Query: " . mysql_error());
}

$num_rows  =  mysql_num_rows($result);
echo "<br /><b>Results returned:</b> $num_rows\n";
echo "</div><table width=\"100%\" cellpadding=\"2\" cellspacing=\"0\">";
if ($num_rows > 0)
{
    while ($row = mysql_fetch_array($result))
      {
    $row_color = ($row_count % 2) ? $color1 : $color2;
    echo '<tr bgcolor="'. $row_color .'">
          <td>      
          <h1><a href="pet-detial.php?id='. $row['id'] .'" target="_blank">'. $row['title'] .'</a></h1><br />
          <h2><b>Pet Name:</b> '.$row['name'].'</h2><br />
          <h2><b>Posted By:</b> <a href="profile.php?id='. $row['id'] .'" target="_blank">'.$row['username'].'</a></h2><br />

              <p>'.$row['description'].'</p>

              <b>Added on:</b> '. date("F j, Y, g:i a", strtotime($row[date])) .' &middot; <b>Category:</b> '.$row['category'].' &middot;
 
          </td>
              </tr>'."\n";
          $row_count++;
    }

}
else
{
      echo "No resources in this category.";
}
echo "</table>";
?>
</body>
</html>

That is my code for pets.php which displays them.

Would I do something like?

<label>Select Parent Category:</label>
    <select name="parent">
    <?php
    $query = "SELECT cat_id, category FROM categories WHERE parent_id=0";
    $result = mysql_query($query) or die(mysql_error());
   
    while ($row = mysql_fetch_object($result))
    {
      ?><option value="<?php echo $row->cat_id; ?>"><?php echo $row->category; ?></option>
      <?php
    }
    ?>
    </select><br />

Which will displays all of my main categories which is stored in cat_id as the ID # and category char as text.

Then do the same for maybe? subcategories?

Any suggestions, thanks.