Authentication in SharePoint 2013 Extranet

Scenario:

SharePoint 2013 set-up on cloud i.e. Windows Azure Virtual Machine and not SharePoint online. This environment will host Extranet sites that will have custom solutions in it.

What is the best way of authentication that can be planned for this environment? 

If I go for claims based authentication, will the custom solutions using managed CSOM code work without any issues? [I remember working on SharePoint 2010 claims authenticated environment and the custom solutions that had managed CSOM code failed, although the user was logged in thru windows authentication]

Thanks Arut