My level of experience with Google Apps is minimal at best. I have used Google Docs and Blogger the most and have really felt the benefit of these apps. I'm pretty comfortable at learning new things and hope that I can learn many new computers techniques through my Computer Technology in Education class.
I feel that the best Google Apps to use for an Elementary school teacher would be, Google Calendar, Google Docs, Youtube, Gmail, Contacts, and Photos. All of these apps can be used for communication and for teaching. Also, with photos you can document what is happening in your class and share it with parents on the class blog.