Had a fresh look at it and got it working nicely right away. Just for anyone's reference, here's the code I'm using (Magento 1.8):
// Mage init
require_once '../../app/Mage.php';
umask(0);
Mage::init('default');
Mage::getSingleton('core/session', array('name' => 'frontend'));
// Get customer session
$session = Mage::getSingleton('customer/session');
// Get cart instance
$cart = Mage::getSingleton('checkout/cart');
$cart->init();
// Add a product (simple); id:12, qty: 3
$cart->addProduct(12, 3);
// Add a product with custom options
$productInstance = Mage::getModel('catalog/product')->load($productId);
$param = array(
'product' => $productInstance->getId(),
'qty' => 1,
'options' => array(
234 => 'A value' // Custom option with id: 234
)
);
$request = new Varien_Object();
$request->setData($param);
$cart->addProduct($productInstance, $request);
// Set shipping method
$quote = $cart->getQuote();
$shippingAddress = $quote->getShippingAddress();
$shippingAddress->setShippingMethod('flatrate_flatrate')->save();
// update session
$session->setCartWasUpdated(true);
// save the cart
$cart->save();