Matte screen protector with hard nib
I use a matte (anit-glare/anti-fingerprint) screen protector on both my note 12.2 and my note 10.1 (2012) with the hard plastic nib on the s-pen (not the soft rubbery one). The texture of the matte screen protector make it feel more like writing on paper.
When using the bare glass (no screen protector) I prefer the writing experience of the rubber nib on the s-pen because it gives the right amount of resistance to emulate writing on paper. However, my palm sometimes sticks when I try to slide it (depending on the amount of moisture on my hand).
I prefer to use a matte screen protector because my palm never sticks (even if my palm is sweaty). However, the rubbery nib causes too much resistance for the s-pen with the matte screen protector, so I use the hard plastic nib instead (which is just right).
Visually, the matte screen protector decreases the clarity of the screen and reduces glare. There is still some glare in extreme environments and I don't notice the degradation in visual quality. Ultimately, I use the notes for handwriting so I don't care about the visual effects of the screen protector either way.