Hi,
Seems like you've read the web docs:
https://www.openmicroscopy.org/site/sup ... cData.html ?
This seems to mostly support what you want, since the 'Public' user only has read access to other user's data in a read-only group. It should be noted that this is purely a web framework work-around that automatically logs-in any anonymous visitor to certain web pages. It is not intrinsic to OMERO server itself.
The OMERO permissions allow any user (including the web Public user) to create their own Projects, Datasets, import Images, run scripts on other user's data etc. These actions can be prevented from within the web by using a regex to filter the 'Public' urls.
So, a lot of what your 'public users' can do depends on how they access OMERO: Web? (or insight?). If web, do you intend to extend the OMERO.web framework with your own UI (For examples see:
http://odr.stowers.org/websimr/ or
http://jcb-dataviewer.rupress.org/) or simply provide links to the image viewer from 'external' pages, E.g.
http://users.openmicroscopy.org.uk/~rkf ... _demo.html