Keeping GMail invalidates almost all the other efforts. That is the frist element of Google addiction that needs to go away. GMail is tying you down to Google and is unfortunately hardest to break free from. My choice (at least for now) is Fastmail.

Disclaimer: I feel strongly about this topic [1] and think that most of HNers should too.

[1]: http://www.ikusalic.com/blog/2013/06/04/case-against-google/