Invalid Method addFieldToSelect in Magento

In your resource model Website_Warranty_Model_Mysql4_Warrantydata you need to add this method :

public function _construct(){
    $this->_init('warranty/warrantydata', 'entity_id'); //the second parameter must be the primary key in your warrantydata table. If it's not `entity_id` then change it
}

and in your model class Website_Warranty_Model_Warrantydata you need this method:

public function _construct(){
    parent::_construct();
    $this->_init('warranty/warrantydata');
}

To answer the question. You would use this (not very different than your version):

$productCollection = Mage::getResourceModel('catalog/product_collection')
                        ->addAttributeToSelect(array('name', 'image', 'price'))
                        ->addAttributeToFilter('status', array('eq' => Mage_Catalog_Model_Product_Status::STATUS_ENABLED));

Mage::getSingleton('cataloginventory/stock')
    ->addInStockFilterToCollection($productCollection);

$this->_productCollection = $productCollection;

But I don't know exactly what causes your error, because it seems related to the fact that the getSubmitUrl/getAddToCartUrl product param is boolean false, and not to the collection per se.