Get the mini or the Air. It depends what you plan to do with it. If using only for travel outside your home, the mini is a lot lighter and easier to carry around. If using it while sitting around the house, go with an iPad Air.
Next time you visit an Apple Store, or anywhere that sells these (including Costco), take the mini and physically put it on top of the Air. You might be surprised how little size difference there really is now that they've made the Air smaller. I've done this with a few people in the last year, all of whom thought they wanted the mini and ended up buying the Air. There's also not a huge weight difference.
Of course, the mini is a great size and very applicable to many people.
Tech specs spell it out, but I've noticed many need to see this comparison in person before they realize the larger unit really isn't that much larger. The Air is also thinner.
The iPad mini 3
Height: 7.87 inches (200 mm)
Width: 5.3 inches (134.7 mm)
Depth: 0.29 inch (7.5 mm)
Weight: 0.73 pound (331 g)
The iPad Air 2
Height: 9.4 inches (240 mm)
Width: 6.6 inches (169.5 mm)
Depth: 0.24 inch (6.1 mm)
Weight: 0.96 pound (437 g)
Sent from my iPad