To get the tax rate you need to perform a tax request. That can be done with the following code.
$store = Mage::app()->getStore('default');
$taxCalculation = Mage::getModel('tax/calculation');
$request = $taxCalculation->getRateRequest(null, null, null, $store);
$taxClassId = $product->getTaxClassId();
$percent = $taxCalculation->getRate($request->setProductClassId($taxClassId));
Here you take the store and make a tax calculation request. You can also specify shipping address, billing address and customer tax class id but in this case I have set them to null and it will take the default values set-up in the admin configuration tax section.
You then take the tax rate request object and assign the product class id, which you already have and then you can ask for the rate itself.