All iPad minis have an 8 inch screen. There is not a 7 inch option.
A big thing to think about on the Apple vs. Android (kindle fires run android based software and use android apps) - what type of phone do you have? If you have an android you may want to go with an android tablet - then you can share apps between your tablet and your phone. Same goes for the iPad mini. If you have an iPhone the iPad and iPad mini can be twinned to your phone. I have an iPhone 6 and an iPad mini 3. I love being able to answer texts and answer phone calls on my iPad mini when I'm using it instead of getting up and finding my cell when I hear it go off. Once twinned your calls and texts will automatically go to the iPad as well as your cell - even if only running on wifi (you can have your iPhone be a wifi hotspot for your iPad if traveling instead of paying for cell service for the iPad.) I don't have an android tablet or phone, but when researching what I was going to buy read that if you have a Samsung phone they can also be twinned with a Samsung tablet. The deciding factor for me on what to buy was that I had the iPhone and I could share apps and music and twin it.
If you do decide to go Apple, I would skip the iPad Mini and go with the iPad Mini 2 or Mini 3. As PP mentioned the big difference between the mini and the mini2 and mini 3 is the processor and speed. At the price you are paying for an Apple product you don't want to go more than one generation back in processor speed - DH went back two generations with his iPhone and after 18 months found he couldn't update his iOS because the processor couldn't handle it and that meant he couldn't upgrade many of his apps and some of the features stopped working. The mini 2 and mini 3 have the same processor but this processor is already a generation old with the mini 4 now out. If you really want a mini 2 I think you are going to find that the mini 2 is going to become hard to find as they will soon discontinue making it, if they haven't done so already, especially with Christmas fast approaching. Apple stopped making the plain old mini about a year ago and anything you find that is new is actually been sitting on the shelf for over a year. Another thing to think about if going Apple. They don't have expandable memory. If you do decide to go Apple make sure you get enough built in memory (for storage, not processing speed). I went with the mini 3 not because I wanted the touch ID but because I wanted the 64 GB of storage.