I would suggest using all the apps that your phone comes with first. Then try out the Google apps for whatever you need. I think this will actually suffice for many people. It is often very very commonly overlooked, but Google apps are superb in terms of integration, usability, and functionality. For drawing/writing try out the note/sketch app included before going on a downloading spree...they work very well on my Note 10.1.
Nothing beats Gmail, Google Maps, and Chrome (at least for me). I also use Yelp, Evernote, Google Keep, Google Finance, and Google Translate quite often. Recently I've been trying out Hangouts and it works pretty seamlessly (texting/google voice calls).
I also use my banking app, Dropbox, and Circa (news). The Yahoo news app is also quite popular. For more customization you can try out feedly.
More of fringe apps (as mentioned above, dependent on user) would be for me, Duolingo (learn foreign language), along with medical reference texts and apps that I use for school. AnkiDroid is also a very good flashcard program.
I don't really play games on my phone so I don't have any loaded at the moment. With the bigger screen and battery life that may change
Then there are tons of other apps I'm sure many people use like social media apps (Twitter, SnapChat, Facebook, Instagram, etc), video/movie apps (Youtube, Netflix), ebook/audio book apps (Audible, Kindle, Newstand), forums (Reddit, Quora), music (Songza, Spotify, Pandora). Really...anything you can think of it's probably there.