I would like to have somes informations about internet public site.
What topoly is recommended ? (extranet topology seems to be the best).
Is there best practice about sharepoint configuration ?
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Microsoft has a bunch of different designs for extranets : http://technet.microsoft.com/en-us/library/cc263513.aspx
I have a sharepoint extended application . The default port is used by our internal users and the extended application makes use of the ADFS and SSO for external users to login to the application . The content is managed by internal admins and made available to the external users using publishing content .
You need to find the number of users accessing the internal/external application . This will make you decide on what farm topology is best suited for you .
There are couple of things to think before to design the public site.
Many companies in industry using the Intranet sites and then publish few content to public using Content deployment. In this case you have two farms( authoring & publishing). people can edit the stuff at authoring site then published to the public site. everybody having read access to public site. this is secure way to publish the stuff on the public site.
you can have Public DNS which directly land on your sharepoint server so people directly access it( i dont like this idea).
you can also think about extending the web app to different zone and use different authentication for this zone.
this question also give you another way of thinking. Intranet & Extranet in SharePoint 2013