I've used lots of different screen protectors over the years, and was never completely happy with one until I got my Tab 2, and used a screen protector from this same company:
Amazon.com: Ionic Samsung Galaxy Note 3 Screen Protector Film Invisible (Clear) (3-pack): Cell Phones & Accessories
This one went on my N3, and it was very easy to get a bubble-free application.
It does not "kill the visibility of the screen" as one reviewer put it. If I handed you my N3, you wouldn't be able to tell it was there until you saw the cutouts for the sensors/camera.