I was feeling more and more dependent on one company's goodwill. A few months ago, I renewed my Fastmail [1] account for 3 more years, being very happy with the service. I use DuckDuckGo [2] as my main search engine and love it. I use Opera as my main browser. The only Google services I use regularly now are Android and YouTube. YouTube being totally optional and Android only being an interface to data located elsewhere, I feel free. Sure, Google has access to my data, but they can't lock me in.
One thing you will notice immediately is that the battery life lasts much much longer. With casual surfing, watching video clips, playing casual games and Wifi always on, the battery lasts for almost 24 hours. It looks as if this is what the original Nexus 5 should be. All those background Google services and "frameworks" constantly calling back home will drain the battery to the death pretty fast. That's also valid for some other apps. Not having Facebook app installed will increase the battery life too.
Sure you have no Google Play store installed but you can always use one of those (safe) apk downloaders like Raccoon[1] or such to login to Play store and download your previous apps. As for other Google services (Maps, YouTube, Translate, GMail, etc.), I can always visit their sites in incognito mode. You will actually realize you really don't need all those individual apps to use these services. They all work good enough in a browser window.
[1] http://forum.xda-developers.com/showthread.php?t=1715375
It also is probably worth noting that, while Apple is plenty evil in its own ways, if you're looking to avoid the rampant data collection of Google, Apple is significantly better in that regard.
https://play.google.com/store/apps/details?id=org.dmfs.calda...
For writing and other docs, I personally use Dropbox but I know that is not the same as working in the browser itself.
Etherpad, Ethercalc and Mailpile (and more!) are all available on top of Sandstorm [https://sandstorm.io/apps/] - which basically makes it easier to manage them all.
It still surprises me a little that there is no web-app capable of editing ODF files. This would allow the email/calendar etc concept to be carried over - host the content (in this case files) on a server in version control, and allow users to either keep an offline copy that syncs, or access via a web app.
From a personal usage view, I disagree with your statement that Apple is no better than Google. No, their software is not open source and doesn't run on any device you want. But their software is also not intended to capture all your personal information and use that to show you more ads. It's basically a perk for using their hardware.
EDIT: and K-9 (for Android) as mail-client.
Either Chrome or Firefox or something else. Choose your poison. One's life has to be depended on something.