If you're looking for an Android phone with a big screen, the Galaxy Note 5 is probably your best choice. It has a gorgeous display, a great camera, and Samsung's stylus is optimized to work well with its version of Android. For example, pulling the pen out of its holster launches a special menu for apps that work with the stylus.
This year's Note is better than ever, especially since Samsung improved its design so that it matches that of the Galaxy S6. You can also write on the screen even if the display is turned off, which makes it easier to quickly jot down notes. Samsung's newer phones also work with Samsung Pay, which works at any cash register, regardless of whether or not it supports NFC.
Price: Around $700