If you are not paying any interest in hosting or managing a web server, then WordPress.com is the way to go. This is because WordPress.com is free, and setup can be done quickly and easily. However, it will charge you to remove the term WordPress, which will be included in the URL, and you will not be competent enough to upload custom themes and plugins without prior payment for the services. You also cannot edit or modify the backend PHP code.
WordPress.org is a self-hosted version and provides additional flexibility with control on your site. Your self-bought domain name can be used, and themes can be uploaded, plugins can be incorporated. Hence, this gives flexibility and custom control to your web development.