Should I buy a screen cover and case for my iPhone 16 Pro?

Why not? I have an iPhone 16 pro max and a Body glove brand case with a built in screen protector. It’s fairly cheap-$20 usd and is waterproof and easy to install.

Yes if you want to protect it.

A screen cover and case will protect the phone.

If that is what you want to do, then you should consider buying these accessories.