Here’s the homescreen of my main Android phone (with some obvious apps omitted, e.g. Phone, Flashlight etc):
Google Voice Search—I use it all the time for setting alarms and adding tasks to Wunderlist inbox.
Google Fit—mostly for making sure I walk my 12000 steps every day.
Opera—I use it instead of Chrome because it’s the only browser that reflows text when zooming in.
Wunderlist—an essential GTD app which I hate. I’m working on my own todo app to replace it.
Barcode Scanner—to grab articles from the desktop PC to the phone via the QRCode Chrome addon.
Google Docs—for work, use it all the time.
Kindle—I read all my books via the Android Kindle app. I stopped byuing paper books years ago.
Dropbox—I like to have all my files accessible to me at any moment.
Trello—I use it a lot, for work projects, hobby projects, self-improvement and Internet bookmarks.
Workflowy—Was on hiatus, but I came back to it recently. It’s an excellent thought capture tool.
Evernote—for note-taking (all non-actionable reference stuff goes here). I use premium, PIN-protected.
Slack—an excellent chat for work.
Some of the apps I use (Trello, Workflowy, Google Docs) are in your “not used” or “second-tier” bins, but I find them absolutely indispensable.
Another point is that I use mostly cloud-based apps, so if my phone gets lost or stolen, I still have access to my data. The phone is essentially disposable.
I think Evernote should integrate with Google Now perfectly well. If Wunderlist does that, Evernote must do that as well. Here’s an article that implies that this is possible: http://lifehacker.com/5992572/save-a-quick-note-to-evernote-gmail-and-other-apps-with-androids-voice-actions (and here’s another one: http://www.getproductivefast.com/2013/03/google-now-voice-notes-to-evernote.html).
As for the text skills, try to use gesture typing or Fleksy. I prefer gesture typing on the stock Android keyboard on Nexus 5. If I remember correctly, Swype (the original gesture typing keyboard) is included with Samsung version of Android.