So if they select 'cats' you want to redirect them to 'cats.php', etc.? Maybe if they select 'something weird' you want them to go to 'weirdness.php' (that's just to show that the page name might not be the same as what's selected).
$redirect_array=array(
'cats'=>'cats.php', //The first part is the form field sent back by the select element
'dogs'=>'dogs.php',
...
'something weird'=>'weirdness.php'
);
Assuming the select element is named "topage":
header('Location: '.$redirect_array[$_POST['topage']]);