The Kindle reading app is available to nearly every device you can buy. Having said that, I would go with a Nexus 7 and install the Kindle app when it arrives. Kindles are extremely proprietary. Amazon does not play well with most device manufacturers. I have a Kindle Keyboard, Kindle Fire and a Fire HD. I am nearly ready to toss the HD through a brick wall after four months. I purchased a Nexus 7 (2012) from Office Depot yesterday and see that it surpasses the Fire HD by miles, while still being able to read my library through Whispersync from all devices I read on.
If you purchase a Kindle, you will need to have, or open, an Amazon account, provide debit/credit card info and go from there. If you intend to side load only, the Nexus 7 is the answer you seek.
Unless you own an Apple desktop or MacBook, or Apple laptop, stay away from the iPads. You'll need credit/debit access for those as well.
Having said so, you need to be 18 years old to acquire any type of debit/credit card. "Legal agreement" statutes apply and require an adult to own such things.
There you have it.