I would like to build an application in Google App Engine (Python) that would be fully connected to a single GMail account and then filter e-mails from this account (e.g. filter messages for a certain string and show it on the string). In the future I am also going to implement the option to send messages.
What is the most efficient way to do this (solution provided by Google if possible)?
What do you mean by "fully connected"?
It's possible to set up a GMail filter to forward emails to a different address (say, the email address of your App Engine app). And an App Engine app an send emails (say, to a GMail address). The trick is to set up the GMail filter carefully to avoid loops.
Filtering GMail messages in Google App Engine application