It's a rather extensive process to do this, but here's a trimmed down version of the code that I generally use.  I won't necessarily guarantee that it will run as shown since I ripped out a bunch of internal stuff that we do along the way, but these are the pieces you need to do it.

You'll need to look at tables `#__categories` and `#__content` to get all the fields you want to populate and add them to the given `$category_data` and `$article_data` arrays.

I should mention that you *could* accomplish it inserting the records with jDatabase or jTable, but I'd not generally recommend that because the important thing that you'd be missing is the built-in Joomla rules and logic that do things like checking the uniqueness of the alias, and managing the ACL for the new content items.

    if (!defined('_JEXEC')) {
        define( '_JEXEC', 1 );
        define('JPATH_BASE', realpath(dirname(__FILE__)));
        require_once ( JPATH_BASE .'/includes/defines.php' );
        require_once ( JPATH_BASE .'/includes/framework.php' );
        defined('DS') or define('DS', DIRECTORY_SEPARATOR);
    }
    $app = JFactory::getApplication('site');

    $category_data['id'] = 0;
    $category_data['parent_id'] = 0;
    $category_data['title'] = 'My Category Title';
    $category_data['alias'] = 'my-categegory-title-alias';
    $category_data['extension'] = 'com_content';
    $category_data['published'] = 1;
    $category_data['language'] = '*';
    $category_data['params'] = array('category_layout' => '','image' => '');
    $category_data['metadata'] = array('author' => '','robots' => '');

    $category_id = createCategory($category_data);
    if(!$category_id){
        echo "Category create failed!";
    }else{
        $article_data = array(
            'id' => 0,
            'catid' => $category_id,
            'title' => 'My article title',
            'alias' => 'my-article-alias',
            'introtext' => 'My intro text',
            'fulltext' => '<p>My full text</p>',
            'state' => 1,
            'language' => '*'
        );
        $article_id = createArticle($article_data);
        if(!$article_id){
            echo "Article create failed!";
        }
    }

    function createCategory( $data )
    {
        $data['rules'] = array(
            'core.edit.state' => array(),
            'core.edit.delete' => array(),
            'core.edit.edit' => array(),
            'core.edit.state' => array(),
            'core.edit.own' => array(1=>true)
        );

        $basePath = JPATH_ADMINISTRATOR.'/components/com_categories';
        require_once $basePath.'/models/category.php';
        $config  = array('table_path' => $basePath.'/tables');
        $category_model = new CategoriesModelCategory($config);
        if(!$category_model->save($data)){
            $err_msg = $category_model->getError();
            return false;
        }else{
            $id = $category_model->getItem()->id;
            return $id;
        }
    }
    function createArticle($data)
    {
        $data['rules'] = array(
            'core.edit.delete' => array(),
            'core.edit.edit' => array(),
            'core.edit.state' => array(),
        );

        $basePath = JPATH_ADMINISTRATOR.'/components/com_content';
        require_once $basePath.'/models/article.php';
        $config = array();
        $article_model = new ContentModelArticle($config);
        if(!$article_model->save($data)){
            $err_msg = $article_model->getError();
            return false;
        }else{
            $id = $article_model->getItem()->id;
            return $id;
        }
    }