Big variations in screen protectors-- by type, quality, adhesive, brand, and price.
Ant-glare, often rainbow effects or slight distortions.
Crysal clear, often some glare but text excellent..
Sticky, cling, spray on, etc... different methods of attachment; some more prone to bubbles than others, some easier to install than others.
Many say that Power Support is the best; in my experience, they are quite good, albeit $$. Their customer service is excellent. I use a Crystal Clear on my iPad and iPhone--superb, not aware they're on save for imperfect adhesion in one corner; the anti-glare produced noticeable degradation in image, as many do, and I took it off.
Joy Factory supposed to be good; they provide 2 in a package. I have a pack for an iPad 2 that I haven't used.
Mixed reviews on many; some swear by Zagg, others swear at it.
You do get what you pay for; at least, don't go too cheap on this!
Having said all that, I, too, would be interested in hearing from people who have gotten protectors for their iPad minis! Things may vary in the smaller size; there could be a newcomer on the block; some cheap import may have become acceptable or even good.