Scenario below:
They only get Authenticated access to view a few areas. How can I suppress the toolbar for certain user groups? or what is the best approach to this?
The simplest approach will be using CSS. You can provide a conditional CSS that hide the toolbar:
#plone-toolbar-container {display: none}
A very simple approach for this is described in this article: http://datakurre.pandala.org/2015/05/plonecustom-for-plone-5.html
Please note: the toolbar contains also a section to personal preference, so removing it will also hide some user's features.