Plastic Screen Protectors
These next three options don't have specific brands attached to them, simply because there are so many of them and pretty much any company and model you choose will get the job done just fine.
So with plastic screen protectors, these are probably the best option for those that just need basic protection at a low cost. If you're just a casual user and want some piece of mind when it comes to your iPad mini's screen, getting a cheap plastic screen protector is a good way to go. You can usually get a multi-pack for less than $10, or you can try scouring eBay to get a pack of them for less a couple of dollars from China.
And don't worry about the quality between different brands of plastic screen protectors. Pretty much all of them are identical and use the same materials. However, name brands like Spigen, Anker, and Tech Armor usually include extra goodies to get the job done, including a microfiber cloth, a squeegee, and dust removal tape.