Why don't you just code the menu to return the menu_type??
<a href="whateverURL.php?category=A">Clothing</a>
<a href="whateverURL.php?category=B">Sports</a>
<a href="whateverURL.php?category=C">Disney/USJ</a>
Then:
$category = $_GET['category'];
$sql ="SELECT * FROM Products WHERE menu_type = '$category'"'
No need for table joins for this simple task.
I would advise NOT to include your php variable within the sql query, that's a security risk and open to sql injection attacks on your database. You should be using sql 'prepared statements'. Anything that a user can potentially alter through a $_GET or a $_POST input field request should never be included directly within an sql query.