This keeps all your data and most settings intact, so you can use your phone as you do it (though it will spend a lot of time 'optimizing apps') or stop and go out :-)
You don't need to unlock the boot loader, so the camera quality stays awesome, and you get all the bundled apps, along with the Google ones.
Use the built in update app to go from 4.4 to 5.
Then use the settings, about, update menu to update to 5.1 latest.
Install Kingroot (I used 4.8) and let it root your phone.