Just use the standard Drupal login form but then alter the redirect once logged in with hook_user_login:

function hook_user_login(&$edit, $account) {
  $edit['redirect'] = 'node/123';
}

Of course you will need to give authenticated users the permission to see unpublished pages.

Giving users permission to view unpublished content could potentially be a security risk, and it's not (easily) possible to restrict it to just viewing a particular content type.

Why not publish the node, but only allow users with a certain role be able to view them using the Content Access module.

Then create a few accounts with this role, setting the usernames and passwords yourself.

Then just use the standard Drupal login form but then alter the redirect once logged in with hook_user_login:

function hook_user_login(&$edit, $account) {
    if (in_array('your_role', $account->roles)) {
        $edit['redirect'] = 'node/123';
    }
}

By creating the accounts this way it means you can use the main Drupal authentication system so reducing the amount of work that you need to do...