Forms authentication and SharePoint Designer

The SharePoint designer always works with Windows authentication mode only. So, if you have converted your site to use forms authentication, you will not be able to open in the designer.

Hence, even if you are going to have an Internet facing site, the best practice would always be to have your default zone site with windows authentication and extend this for the Internet zone.

Steps to do this is available all around the place, check this for a start.

http://technet.microsoft.com/en-us/library/cc262668(TechNet.10).aspx