Some people are screen protector users, others aren't.
If you want to use a screen protector, try and find one that will not interfere with the Apple Pencil, if you purchased an Apple Pencil or decide to try and purchase one in the future.
I have never used a screen protector on any of my iPads.
If you keep the screen clean and screen covered closed when not using your iPad, you really do not need to a screen protector on an iPad.
But I am staying completely neutral as Switzerland on the topic of screen protectors.
iPad screens can still get damaged/cracked even with a screen protector applied.
Someone who reviewed the Zugu case mentioned that the case fits too tightly with a glass screen protector on an iPad/iPad Pro so if you use a screen protector with the Zugu case, maybe purchase and try a thin film plastic screen protector, instead.
This is your decision.