im re-factoring php on zend code and all the code is full of $_GET[\"this\"] and $_POST[\"that\"]. I have always used the more phpish $this->_
Extending Brian's answer.
As you noted you can also check out $this->_request->getPost() and $this->_request->getQuery(). If you generalize on getParams(), it's sort of like using the $_REQUEST superglobal and I don't think that's acceptable in terms of security.
Additional to Zend_Filter, you may also use simple PHP to cast the required.
E.g.:
$id = (int) $this->_request->getQuery('id');
For other values, it gets more complicated, so make sure to e.g. quote in your DB queries (Zend_Db, see quoting identifiers, $db->quoteIdentifier()) and in views use $this->escape($var); to escape content.