As mentioned earlier, if you want a screen protector but don't want to lose that signature feel of the glass display on the iPad mini, then getting a tempered glass screen protector would be perfect for you.
Tempered glass screen protectors come in thin sheets of glass that you simply affix atop your iPad's screen. They're a bit thicker than regular plastic screen protectors, so the Home button may feel more recessed than usual, but that's something you can easily get used to.
One thing to be aware of is that tempered glass is a bit more expensive than other screen protector options, simply because it's glass and not just plastic, but it's highly worth it if you want to keep that premium glass feel when using your iPad.
Tempered glass screen protectors aren't as common as cheaper plastic options, but there is still plenty of selection out there. This one from Tech Armor is a good choice, as it comes with a lifetime warranty.