Is there a shortcode for a simple registration form?

Yes, this is a feature provided by s2Member Pro Forms. Once s2Member Pro is installed you can navigate in your Dashboard to s2Member → PayPal Pro Forms (or whichever payment you integrate with) → Free Registration Pro Form.

There you will find all sorts of Pro-Forms that you can use, including one that simply allows a user to register on the site without going through a checkout process. You can also control the Membership Level that the registrant will be assigned to, and a few other things too :-)